This is a trick I used with my son... Pick some of her favorite cartoons, movies, etc. I would ask my son, "Who are we going to brush tonight?" He would pick some cartoon, say Winnie the Pooh. Then we'd get excited about getting the "sugar bugs" off of Pooh & his friends. I'd ask him, "OK, where's Pooh?" and he'd respond by opening his mouth and pointing to, say the upper right side (or wherever). Wherever he pointed, that's where we'd brush. When that side was done we'd ask, "OK, now where's Tigger?" and repeat the process with different characters in different locations until each section of his teeth were brushed. He loved it and would laugh while we did it. Just try to use different characters, animals, etc to make it a little differnt each time so it seems more fun.
And I agree, it's better if she doesn't swallow the fluoride toothpaste. It's not terrible, but try using the fluoride free until she can spit it out better. There are several childrens training pastes out there that are fluoride free. Good luck to you and let us know if you come across a secret trick!