Are you keeping a journal/calendar/documentation of all of this?
At least now you know that his sister, while probably well-intentioned, can't be relied on or trusted. I had a very similar issue with my ex's sister - she seemed well-intentioned and was a help for a while (sort of...), but in the end she was still very much enmeshed in the family dysfunction, which ended up causing more drama and trouble for me. I am "no contact" with her now.
It seems like the ball is in their court now. If the grandparents want to see kiddo, they know how to contact you. It's time for you to work on your anxiety about all this (believe me, I get it - I have been in very similar circumstances) and set some boundaries.
While my ex was homeless/MIA, I would meet him at a local playground for about a hour each week. He would hang out with the kids, I would read and watch from the parking lot, and the kids would play. One of my boundaries was that I had to have at least 48 hours' notice before we would meet.
Good luck, and keep us posted.