Wow, I'm so sorry you have to deal with this.
Please, do yourself a favour and read and re read the posts by Mike7, Stronger08 and Years of Pain.
This is just an untenable situation which ever angle you look at it from, and I'm sorry, with respect to JFO, I can't see it working out any way but badly for you.
You have so very little to work with right now, other than your desire to still have your marriage and your wife.
It takes a total mind change to realize that what you had has gone, and it's a painful process, but at some point your pain will be replaced with resentment, anger and frustration.
Look at what you have in front of you right now;
Wife having an affair
Wife prepared to risk contracting disease by having unprotected sex, both to herself and to you
Wife pregnant by another man (OMG)
Wife not willing to immediately end all contact with OM
Wife not showing any signs of remorse, just regret that she got found out due to her own carelessness
Wife only giving lip-service to the pain and trauma she's inflicted on you, if this hadn't come to a head by her becoming pregnant, how long do you think she would have kept cheating with the OM?
Wife giving you the ILYBINILWY speech - however after a short two months she's "in love" with the OM
Wife prepared to risk the future stability of her children with you
Wife prepared to possibly have a marriage of convenience with you (she gets your home, your income, your support and her boyfriend)
Wife's OM being a constant feature in your life going forward, he's not planning to go away, and even if it's sporadic contact, he's another constant reminder of your unfaithful wife's behaviour,
And that's just a few, factor in your mental well-being, your pride, your self-esteem... all these have and will take a continued direct hit as long as things stay the way they are.
The idea of trying to form a blended family in this way is simply nuts IMO, have you thought about the drama you will have to face all the time? Picture school events for example, you, her, your kids, their kid, and him..... just nuts.
Your own children are very young, they can adapt to mum and dad having different houses, they won't thank you for forcing them to live in a situation where they have to explain their half-brother/sister constantly.
Your wife should not be vacillating between you and him, and for your own self-respect, you shouldn't let her.
So far this is all about her, and him, not much about you, this needs to change. You need to take control even though it goes against what you feel, you won't nice her back, you won't love her away from him, you can't control her.
But you can control how this plays out for you, get some legal advice, turn off her financial tap, draw a line in the sand and stick to it. Find the 180 in the healing library, read it and live it, it will make you stronger and better able to make the right decisions for yourself and your kids - she's incapable of doing that right now.
I'm sorry if I come across harsh, but believe me, I only have your best interests at heart, and from the outside looking in that's how I see it.
Please take care of yourself, this is trauma like no other, try and stay healthy, eat, drink water, sleep, we're all thinking of you.