If the tie was only days ago, then I think she should be able to have a spay
right now.
Talk with your vet immediately. I cannot imagine why you let her go to her
3rd heat without spaying anyway, knowing she is a mixed breed rescue!
The question of why you would let a dog in heat be loose in the yard especially when you KNOW your neighbor has an intact male also begs to be asked!
Two mixed breeds mating -- it is anyone's GUESS what the puppies would look like, but as Mary (Mardelin) said it is highly unlikely any will look like pure yorkies. You said yours is yorkie/chi mix and the neighbor's dog is a chi/maltese -- seems they would wind up more chi than anything but with long hair thrown into the mix. When you are dealing with mixes to start with there is little guarantee they are really a 50/50 mix. Could be ANYTHING. The fact that the main question you have in this DIRE circumstance has to do with how the pups might look is SAD!
You say you are working at Pets at Home and "are trained a lot on dog nutrition and stuff" -- not sure what stuff that might be but didn't
responsible ownership come into the studies anywhere? You say she was not intentionally bred but it does not sound like she was intentionally NOT bred! In other words basic precautions were not taken.
Please see if the vet will spay immediately -- why are you even waiting for a Friday appointment? There is no excuse for bringing convoluted mixes into the world.
I could not muster any sympathy for this one -- you are not doing right by your dog. The idea that you are all excited about a possible litter is also sad. Put your girl FIRST. Get her spayed as soon as safely possible. I hope it is before she delivers a litter.