she will still make more than they can eat for dinner and put in Tupperware and bring to me at drop off. She texts Merry Christmas. Gives me framed pictures of the children as a gift.
Hi Emb. Sounds like you have the basis for a reasonably civil, co-operative and functioning co-parenting arrangement happening. As hard as it is, you need to try to separate your hurt and anger from your need to deal with her regarding the kids. As the youngest is only 4, you're looking at another 14 years of very regular contact with her, and perhaps less regular contact beyond that.
The best possible outcome for your kids is to have a good relationship with both their parents, regardless of whether you reconcile, or one or both of you re-partner. Of course, looking after yourself is critical, not only for your own welfare, but for your ability to effectively parent.
I'd strongly advise
against asking the kids about their Mums' new 'friend'. If they tell you things of their own accord, that's fine, but if you're asking them, that'll get back to Mum and cause more trouble than any information you may have got is worth. More to the point, it's not fair on the kids. They love their Dad and they love their Mum, as it should be, and it's wrong to expect them to "take sides" or "spy" for you.
I know you're hurting, angry and confused, so make sure you make good use of the resources here, Emb.
It's always darkest just before the dawn.