You can ask for 100% custody of your biological kids - she had a handful so that may work. Depending on how old the others are you may want partial custody.
This is what I'd be doing ^
Look, you gotta get over the number of people she's had sex with, and the fact that she has 3 kids from 3 different dads. SFW? You said you wouldn't have married her if you knew that, and that's your right (which was taken away from you) - but at the end of the day, it shouldn't make her any less worthy of being loved (by the right man, which you admit that you would not have been). Anyway, it's a completely moot point, because it's not what this is about.
The real, and only, issue, IMO is that she lied to you about all of this. That's ****ing terrible, TBH. Not only that, but she never told the fathers of two of the kids that she was having their baby. That's awful, and divorce-worthy, IMO.
Look, us dudes need to get off this BS about women having "lots" of sex (or god forbid, getting pregnant) before marriage. We men have been doing this for eons - but we don't get pregnant, nor do we get reputations, so we get to walk away thinking we're just guys being guys. So don't make this about that.
What it IS about is that she did it all on purpose, and hid it from you. She did some dumb **** - which we're all entitled to, and most of us have done - but she didn't OWN it. And that's where this all went off the rails. You were duped, no doubt about it. I'd be out of there, too, honestly. But NOT because she did some stupid **** before I came along. Solely because she didn't own it, and lied to you (and many many others) about it all.