this is just getting weirder and weirder. I know your little guy is really close to your sitter and that he has already had a lot of loss in his young life but I would find another sitter and distance myself from this whole family....even if they are neighbours.
I know you have mentioned that it's hard to find sitters who are affordable but is all of this worth it? Only you know if you can handle this but I would not under no circumstances allow my children associate, let alone go to visit other people who I didn't feel comfortable with.
I also know that you have things set up for the sitter to help you with the little ones birthday this weekend...and that was nice of them to give the kids gifts...but the best gift they could give your family is being more neighbourly to everyone in your family.
I would ask some of your mom friends if they have a reliable, reasonably priced baby sitter that they would recommend and find someone else...or even a few who you could rely on to help you.
good luck with this situation....and enjoy the birthday celebrations this weekend.
Blessings from Hope