Sometimes, events cause relationships to thrive or fizzle out.
It may be that the best option is to do nothing. Explain to the child what is going on and why. If either kid is uncomfortable in the others presence, then that is all that is needed. A decision has been made by the most important person.
In time, (esp considering that the kids are 8) things may change. I would avoid overreacting. Some time apart and some time to cool down isn't overreacting.
Besides, if the other kids parents won't help their child to apologize, you have a great head start with this particular family. You know and understand some limits from the future.
If I were the parent, I would sit down with the other parents, say that our friendship is fine, that these things happen, and that you have decided not to force anything. Wish them well, and go to Burger King.
or...
If you feel an apology is in order, then sit down and explain why. If the other parents are adamant that no apology is forthcoming, then the only decision to make is to what extent you can associate with this family without sending mixed signals to your kids. They trump old friendships.