I agree with BklynMom, you can see how it goes. I know what you mean about the emotions. Every time my H visits or stops by, I’m a nervous wreck. At least in your case, the legal stuff is over and you don’t have to anticipate any conversations about it.
I think he is using the dogs as an excuse to see you. Was he attached to the dogs a lot before the BD? I’m sure he still has some emotions about you. His “new” life is probably not giving him much relieve as he hoped. But, this is just a speculation on my part. If you decide to let him to come over, treat him as a neighbor.
M:50 H:52 S28 (my S from previous marriage) M:17 + 3 BD: 06/12 S: 06/12 - H works in another state