I do not count on my kids' dad to do anything. If it needs to be done, I do it.
I learned that while we were still married and living together, and it was a pitiful thing to have to learn then, but now I just handle it and don't resent him. Except occasionally. for very short periods. when I am feeling sorry for myself.
I just learned how to avoid being disappointed and angered - I don't expect. It is easier to not expect anything from someone you aren't in a relationship with.
It's really about you and what works for you. Him being at your house, picking fights and not helping doesn't work for you, so you might consider figuring out another way for him to see them. Like at a park or something while you run or read.
Based on my experience, it became difficult for me to have STBXH at my home because it stripped my house of its sanctuary-ness. STBXH still acted like it was his space and he was disrespectful to me there.
18 months later, it is so mine and the kids' haven.
Draw your own conclusions.
