I agree with you about the interactions they have that are just between the two of them, though I don't necessarily perceive them as mom-and-dad interactions. I see JJ as Hotch's mini-me, sort of, rather than his other half, like they share a lot of traits rather than having a complementary set of skills. But regardless, I love JJ & Hotch's relationship. There all these little shared things that separate them from the team.

Also, do we know who is doing the case-picking now? Has Hotch re-absorbed that duty from JJ? Garcia might be the one presenting the cases to the team, but I'm certain that she isn't the one picking them. If it is Hotch, that would be another thing that he and JJ share.