I'm in the same situation as your partner's extra curricular relationship. In my opinion it seems very controlling and almost abusive of you to be someone who puts a limit on how frequent your partner is able to be with someone else. It's actually unreasonable. Setting boundaries on how, when, etc... two people want to interact is unfair. Especially if she's getting so little and she probably needs more. Infact I know she needs more. If she's not a real threat, relax, and let them spend however many days together as long as it doesn't dominate your time.
Like she's made the choice of going into this arrangement, you're making a choice by only giving a few days/nights of your time to your partner, and being with your partner in general knowing their Poly needs. Even if you didn't know this until some time into the relationship, you were still made aware of it, and have a choice to stay, or continue fishing. You're not living together, married, or with children together. So, it's a less risk prone situation for you to walk away should this not have been to your liking. If he needs to be more engaged with female company, maybe you should give him more of your time. Perhaps this will shake the Poly webs off of him and give you the Mono attention you require.
In my experience with the man I am with who is Poly... these men generally need to be constantly engaged with a female relationship, whether it be sexual, romantic, platonic, etc... They require that connection to feel good. More often than not the attention they require isn't enough for them and they find other partners to sustain themselves. They also have an ego where they enjoy feeling wanted in every which way. The more dependencies, the more important they feel. Most Poly men are more successful in their careers, they like to dominate, and they like being able to get what they want at a drop of a hat. Most on a MFF level are Alpha Males who instinctively enjoy providing and supporting their partners. Sometimes a quality is lacking in their primary, that quality is something they need, they look for extra curricular activities to find it, but still want to maintain their primaries because they enjoy the qualities that they do have. Some Poly relationships surface because of ones ability and need to share love alone with multiple partners. Not because one partner personally isn't enough, but because they enjoy loving many in an isolated sense. There are also those Poly relationships that exist because someone is obligated and can't bring themselves to fully leave. So, they just add to what they have to get through their days. There are so many motives for these relationships existing.
I find it's due to women being more unavailable because of modern society that these relationships are happening more. Most women won't stop working to stay at home (whether it be their parents house or their house with their husbands - only in the last century has it been acceptable for a single woman to be on her own), even if their partner is well off enough to support both. Polygamy is more dominated by the male. There are more men looking for multiple partners and most of the partners they chose are Mono to them. This I feel is because men are more territorial. I also feel it's safer for paternity should a partner become pregnant. A society that Polygamy is more accepting of is Islam. It goes long before the Mormons. In Islam a man is allowed four wives as long as he is able to support each wife 100% and equally.
I also blame the media for "Sister Wives" and "Big Love" in the increase of these relationships. It looks trendy, cool, and gives everyone a reason to 'cheat' with dignity. I'm not saying I'm anti-Poly with that remark. It's just amusing to see people who've been notorious cheaters transition to being Poly still engaged in cheating ways. Being Poly is about being open and honest with your partners. Screwing around with a few partners and having not one of them know about each other is cheating, not Poly.
I don't know how new you are to this whole world of Poly, but the reason for my banter is to educate you on the motives.
It's largely your subconscious telling you that you're insecure with what you have by being so hesitant. I think it's selfish if you already know your partners tenancies. Limiting his time to feel even better about himself and giving her little of his time to feel good about herself/connected in general will do more damage. If you keep firm with your original wants/needs and they're that crazy about each other... they will rebel, all will be hurt.
You need to allow a balance where not just your needs are met. If this becomes all about you it's not a healthy two way (in this case three way) street of a relationship. Trying to change a person because they're Poly to suit your Mono ways will also never work. These behaviours don't change. You just need to accept it. A Poly person is just as valid as a Homosexual person. It's their human nature. Taking that away from them will be a very uncomfortable transition. Us women have issues with relationships we enter inevitably becoming all about us.
These relationships are so multi layered and resemble an onion in my opinion. They're so complex but at the end of the day you need to give a little bit more to get a lot more. You'll earn more respect by him and especially her. Like in business, in order to make money, you need to spend money.
I wish you the best and please accept my apologies if I have offended you in any which way!