First of all, welcome to the forum. I'm sorry that that the situation that brought you here is causing you such turmoil, hopefully you can find advice and support here.
I'm going to address several points in your post that raise some flags for me as to where some of the troubles may lie. I realize that relationships are complex and it is hard to convey the whole picture in just a short post.
Last summer my husband and I decided to explore poly. We talked about it, and while we have been swinging for a while, I know swinging is nothing compared to being poly but we thought it could be the next step for us. I originally thought this would be something we would do together and explore together.
Many folks come to poly from a swinging background, so this, in and of itself, is not unusual. What I often read here is that a couple tried swinging but found that they were looking for "something more" and find poly.
From what I gather (I have never participated in the swinging community) one of the problems that people run into when making the shift from swinging to poly is that swinging tends to be a fairly "couple-centric" activity...it IS something that couples "do together and explore together" and the assumption is that they will "ease" into poly the same way. It sounds like this was YOUR expectation. (Was it also your husband's expectation? Or did he go along with that idea because it made you more comfortable with the whole poly concept? You don't have to answer, I am just asking.)
Problem is that when the focus shifts from an activity (sex) to a relationship (love) - things get a whole lot more complex and unique. People have individual relationships with individuals - and each one is different. (An example, I have a father-daughter relationship with my Dad. My husband has a FIL-SIL with my Dad. We both have a relationship with my Dad but they are not the SAME relationship. My husband and I can't meld ourselves into one "unit" and be a "daughter" to my Dad together.)
... We originally thought adding a female and becoming a triad would be where we would start and I was ok with that being a bisexual female...
This is very common...and intellectually makes a lot of sense to many people, especially when they are first starting out. The idea is that you find someone who is interested in both of you, you both date her, every one is "even" and you avoid jealously/hurt/anger/etc.
In practice this is very difficult to achieve (as you are experiencing). The most common experience that I see happen here is that if a couple DOES find such a girl it is uncommon that things progress "evenly" in all of the relationships. A Triad is a beautiful thing, when it happens, but it is NOT easy, and is fairly rare (at least in my poly reading). Most successful Triads seem to "just happen" organically, not because people are necessarily "looking for" them.
PS. If you read around here you will run across the term "Unicorn Hunter." This refers to a couple that is looking for a bisexual woman who is equally interested in both members of an established couple (the so-called "Unicorn" - because she is so rare and sought by so many). There is a fair amount of negativity surrounding this phrase so I just wanted to warn you so you don't take it personally.
Then he met this girl. At first when he met her he didn't even mention he was attached. They talked for a couple of weeks and then he randomly sprung me on her, which was completely awkward for both of us.
There have been a number of posts/threads here talking about the "when to tell" decision - and there is no hard and fast rule. For me, if someone was not up front right out of the gate about being attached that would not fly. Others find it presumptuous to assume that someone is interested in you romantically right from the start and to dig into the poly/open nitty-gritty before an interest has been firmly established.
The "springing her on you" bit is also rude and hopefully something that can be avoided in the future. When we first got together Dude sprung one of his "fuckbuddies" on me - invited her to my house! His reasoning was that two bisexual women who were both interested in him would, OF COURSE, be interested in each other....NOT so. Awkward.
She is much younger than both of us. For the first little bit it was ok, not great, but ok. Then we had this night where we were all going out and she had this little freak out in front of me and it just completely turned me off.
Without knowing more about her and the situation it is hard to gauge how this could have been avoided. She is "much younger" than you...does she have any poly experience? (or much relationship experience at all for that matter?) What were her expectations going into this? What was she freaking out about? For instance, some women in this situation might assume that the reason that they are being sought by the guy is that his relationship with his wife is rocky and she is going to "win him over" and steal him from her for her own (in poly terminology this would be a "cowgirl") - Did she suddenly realize that this was not the case?
... I expressed to my husband my doubts, but he kept saying it will be ok and pushed the relationship on. Since then its been a constant source of fighting between us. I tell him I hate this on a regular basis but he says he won't give her up because they have feelings for each other. He keeps telling me he loves me and will never leave me, and while I want to believe him sometimes he just seems so unhappy with me and would rather be with her.
This, to me, sounds like a man caught up in the throes of NRE (New Relationship Energy). This is a time when people can't seem to see straight - they view the world through rose-colored glasses. They are so caught up in the excitement of the "new shiney" possibilities that they can lose sight of what they already have. Especially if they have no experience dealing with this. They can be rude, neglectful, distant...This then, of course, triggers your own insecurities, etc.
I don't have any great wisdom but I can tell you that NRE wears off eventually (6-18 months depending on the person). He will see that this woman has her own foibles and flaws. The rose-colored glasses will come off. (This happens in mono dating as well - this isn't a poly thing - there is a reason that many people end up dating several people before they form long-term relationships.)
If he chooses to come here for advise there is plenty on dealing with NRE without neglecting existing partners. But for you, should you choose to stick it out, I can only advise patience and actually believing him when he says he loves you and will never leave you (as hard as that may be). You are in a hard place, there are no promises as to outcome, only intentions.
I have threatened multiple times to end it for him and he says if I do he will be miserable and I am honestly worried he will leave me.
Hmmm...OK, I don't actually know what you mean by "end it for him" - he is an adult human, he determines his own actions, he can be in a relationship with her without your permission or consent. You only have control over your own actions, i.e. whether you choose to stay in a relationship with him under the current circumstances.
Perhaps you mean that you have threatened to offer him an "ultimatum" of "her or me". In which case, yes, he could, in fact, leave you. If you are not prepared for that possibility you should think long and hard about issuing that ultimatum.
On the other hand, you are certainly within your rights to set your own personal boundaries. If your boundary is "I can't be in a relationship with you under these circumstances - either the circumstances change or I exit the relationship." Then that is the line for you. You get to choose what relationships you engage in under what circumstances, as does he. If those don't match...?
I don't know what to do anymore. The stress of all this is really getting to me. Originally we made a deal that he sees her 3 nights a week and I get 4 nights a week. But every minute he spends with her I resent it. Plus, anytime he has anything else on the go it always takes away from one of my nights, never hers because he claims he sees me more with the daytime hours we spend together.
I don't know what to do anymore. Please someone help me.
Ouch. I can tell how much pain you are in. This last bit deals with time management - I would guess that you are focusing on this because it is something concrete that you can point to, but it is some place to start.
3 nights to your 4 SEEMS like an awful lot - but in the NRE stages people are often driven to spend AS MUCH TIME AS POSSIBLE with their new paramour (so they can't see this as excessive is my point). (PS. I am not one to talk, my Dude has been living with us since before Day 1 - this is not generally recommended but has worked well for us).
My other point is that you, apparently, agreed to the 3/4 split ("we made a deal") and are now finding that you are not OK with it. The fact that "time away" is taken from your time and not hers is almost a moot point (regardless of his arguments) since "every minute he spends with her I resent it". Would this be true if he saw her once a week? once a month? twice a year? Is there ANY amount of time with her that you could (now) see yourself being comfortable with - or is his very involvement with her AT ALL the issue?
(Sorry this got so long, I do that. I wanted to give you some "points to ponder" since I don't have solutions to offer.)
JaneQ