When my own kids were the same age as the kids in care they were often included in birthdy party invites. I think it was nice rather than have a child talking about their party to my child and all the fun they were going to have etc.

I have done a couple of Christenings but for second babies so family had been with me several years. I used it as a chance to meet friends that might have babies too - networking idea. And it went over well with the relatives which actually helped my relationship with the mom and child as now they felt they had approval.

I don't do social outings with just the parents though.