Please look into counceling and work on the communication skills between the two of you. It's understandable that you would need alone time with your wife and your family. Your feeling overwhelmed and oversaturated and all your relationships are suffering. You NEED to be able to talk about this! Others here have said there are multiple relationships here and each need attention.
You and your wife
You and your wife's g/f (even as just a metamour)
The three of you together
Your wife and her g/f
You as an individual (and each of them as individuals)
Now add in each of the kids, etc
If sounds like the relationship between you and your wife has been overshadowed and neglected by the g/f.
I've been through the "OMG! Why is ___ always here. I want my house and family back. I never get to spend any time with you." Let me tell you, the emotional outburst/cut everything off usually doesn't work all that well
. Specifics work better and sometimes you have to just start with one or two changes and build and adjust from there. It's amazing how just getting one of your needs met (that are currently being neglected) can change your outlook on the situation and toward this other person.
Not sure how old your kids are, but as they get involved in 500 activities, even in a mono relationship, scheduling and communication are key. Set a schedule for a weekly date night between you and your wife. Set 3 days that are just "your family". How many days a week do you NEED your house to be visitor free? I can't handle constant company either, but even worse is coming home to find people in my house after work. I don't like surprises, give me a couple hours warning and I do much better. Do you have other activities you are involved with, that are just for you?
A number of years ago, things got so bad that every time I tried to plan a family vacation, my husband would invite this other family with out even discussing it with me. All of a sudden they were coming with us. I finally got fed up with it and had to preface every vacation planning with "this is just for the 4 of us". He got the clue and now I don't have to make that statement anymore.