I have a 15 week yorkie he will not eat his food but if I dump it on the floor he will but he does not eat all of it and it is hard to picup because it sticks to the floor but when I take him to my moms he eats all of her dogs food what should I do

Make sure you get your mom to pick up her dogs food before you visit.
Free feeding is a terrible idea. Dogs should have set times they eat, twice a day, puppies 3-4 times. Leave the food down for 10-15 minutes and anything that doesn't get eaten is picked up. They soon learn that if they don't eat it, they get nothing else.

As for not eating out of a bowl try feeding on a plate. My youngest doesn't like eating from bowls but will happily eat off a plate.

Thanks