You are not being childish or stupid - it's a natural reaction. You said it yourself - hard to get proper closure when there's a child involved. This is part of the grieving process - even though you chose to end it, no-one gets married hoping it won't work out so of course you will feel sadness. Let yourself feel fed up, have a good moan, spoil yourself a little, and then look at the bright sides.
For example: - you are no longer in a toxic relationship so you don't have to put up with his crap - your DD will do better without him living there as a bad relationship doesn't help the children - and she will still see him, plus living with a happier mum - when you move on yourself you will have a much better relationship due to what you learned this time round (and DD potentially a really nice stepdad too) - the ex's ex who you don't like is now having to put up with ex! Revenge!
I split up with my ex partner nearly two years ago. The relationship went very downhill after I had DD (three). I had very bad PND and he behaved quite badly towards me and more and more narcissistic personality traits came out in him and it was my decision to split.
It's been quite up and down since and I've always thought I would be glad when he gets a new partner as it would get him off my back so to speak and give us proper closure, which is hard to have when you have a child with someone and they are still very involved in your life.
However, I found out (not through him being honest) that he is now back with his ex who he has another child with who he has not been with for nine years. This is made me feel very jealous, upset and hurt and I feel as if I'm being unreasonable and stupid for even feeling like this as our relationship became so toxic. She made things quite hard for us when we were together for a while, so there is no love lost between her and me. There's also a part of me that is upset that DD's half sister will get to live with her dad and DD won't.
I know I'm being stupid and a bit childish about this and need someone to come and talk some sense into me as it's really knocked me for six!