OP, you are a magnificent woman and mother. I have to add my voices to the others saying that your H is not a good father, not at all. He has risked their happiness, security and stability (they will continue to have all of these things, but ONLY because of you) for his own agenda. No amount of 'but he's a good dad' will ever cover those tracks.
He has failed at the most basic hurdle of putting his family first, thinking of his kids above all, and has potentially thrown their little world into chaos (again, ONLY because of you will he not achieve this). He is NOT a good dad. He's a bloody awful one.
I think his messages are carefully worded, and he's hedging. He hasn't apologised or begged forgiveness, because - possibly - he doesn't know the detail of how much you know. He's possibly even hoping to get away with 'few drunken shags/fear of impending baby life/similar bs.' Finding out someone you love is this person is catastrophically upsetting, and realising the extent of who they really are will take time.
I'd either continue to ignore, or - my preferred option I think, but others may not agree - just be completely factual and minimal: 'I have instructed a solicitor. They will contact you to deal with matters on my behalf.'
Thinking of you, OP.