I've been in the counselling game a very long time, and believe me, many, many couples IMO that go to counselling already have a marriage that is over.
Your marriage is definitely over and you are hanging on because it's all you know and for this wee baby. It is comforting hanging onto what we know, when we know deep down that some things are better let go.
Seriously, she is using you as a safety net probably in case things don't work out, and holding over you the fact that she is pregnant. And like another OP said, how do you know this child is yours?? This is hurtful to consider, but you already said she was unstable beforehand, and cheaters NEVER just cheat with one person, whether they are married or not.
I wouldn't move near her as she knows she can command what she wants you to do. It will be worse seeing/contacting her every day, and all the hurt will come back. I'd personally just let her go, and get on with your life. What about YOUR health and what this is doing to you? You have to move, you have to pay to move, you have to find somewhere etc etc. What about your own mental health?
And I do think sometimes people use the excuse that 'God has a plan for them' to hold onto something that is obviously not going to work.
I would seriously look at getting your wife scheduled into a mental health unit - the police (in our country; don't know about yours) can do this& take her to Emergency to get assessed, as she's displaying bizarre behaviour. If she's this labile (her moods are up & down all the time) & unpredictable, (meeting and falling in love with internet strangers after 2 weeks was it), she will end up harming her child at some stage. Is she drinking on the side or taking drugs you don't know about? She might need to be assessed for some sort of mood stabiliser, though this would have to be taken into consideration with her pregnancy.
I say all of this with concern not only for your health but hers & the baby: get her scheduled ASAP, get DNA testing for the child and if it is yours, then apply for custody of this child after it's born. This child will be in danger with this woman if you do leave it with her, I can tell you now. I've heard and dealt with people with these very similar stories like this in my career, and some of them have had very tragic consequences through no tough action being taken. And tough, loving action is what you need in this case.
I say this with love: she is seriously leading you on & playing you for a fool, and playing upon your Christian nature, as you are forgiving her bad behaviour at every turn. Even Jesus was hard towards people like the tax collectors, I believe. You can't just keep forgiving extremely labile & very bad behaviour at every turn. With kids we don't do that - they get a suitable punishement, and kids grow up better for having known boundaries.
She knows there are no boundaries with you, so she just thinks oh well he's there - I'll just use him.
Also enlist the help of everybody and the police & legal services. If she is being irresponsible during pregnancy, what will she be like as a Mum? She can also be charged and jailed with child endangerment as well just being pregnant. She needs a strong advocate for that baby. God knows what she is doing to herself and that baby, but I really hope & pray that it is safe.
I do feel for you really but I need to say this up front: this situation is over and it is not about you or your wife anymore - it's about that baby and keeping it safe.
I hope something good comes out of it all for you, I really do.