Anyone that can tell the mother of th4ro child to fuck off, is a nasty piece of work. He views you with contempt. And that's someone you should stay as far away from as possible, permanently.
And it sounds sounds me that he maybe got wind that you were feeling better. Or that you were seeing someone else. And he is like a 2 year old with a toy who puts the toy down but still considers it his.
Either that or there was another woman involved and that hasn't worked out so he is sniffing around you again.
Either way. Sod him. He's a bastard. Lead by example and show tour children that partners do not get to treat us like shit and expect us to come back to them. A healthy, happy single mum is much better for them than one who is being treated like shit.
As for new guy, I only been 6 weeks. Take things really slow. Dont do anything rash like introducing him to your kids or looking for a flat with him. Just treat it as a bit of fun.
You don't mention if abuse was present in your marriage but considering how nasty your ex was at the split, i suspect it may have been..so make a point of researching how to spot abuse (including things that may present early on, like 'love bombing'). Just incase. As it is common to leave one abuser only to end up with another.
My advise would be to focus on making a good life for yourself. I'd say date and have fin but it does worry me a bit that you are talking for falling for someone else so soon after one 4elationshop and oy 6 weeks in.
But so long as you take things slow and don't do anything difficult to take back with new guy then I think its fine.
Tell your ex to shove it though!