Oh what a terrible situation, I'm so sorry you are going through all of this. You had separated well before his uncle's passing, right? And the family has shown zero interest in you or the kids' well-being since then, until this request to help with the desserts. I'd be offended too - it IS offensive (& selfish) behavior on their parts.
I wonder if you have reflected that maybe this is your HP's way of showing you exactly how disposable your AH sees you & your relationship while he is still actively drinking. I mean, "keep you around without any commitment to you OR the kids"???? That is the absolute height of self-centered behavior isn't it? And he obviously has no desire to change it.
As they say here at SR - he's showing you who he really is... believe him.