Flouride is not to make teeth any cleaner, it just makes the enamel stronger, and if she has it in the town drinking water, that is sufficient. I had an overdoese of Flouride as a kid, I lived in the country with well-water, so they had me chewing tablets daily, but then I went to school in town, and drank the water there, and our greade-school had monthly fouride treatments we all did, and we had flouridated toothpaste - I do have VERY hard/strong teeth, and at 31 years old have still never had even one cavity, BUT I do have yellowish spotted discoloration on my teeth (I have never smoked, and I brush very regularly) because of the excess flouride.
My grandpa and uncle are dentists and my Mom, Aunt and cousin are dental hygienists, they all have told me that the action of the brishing is what cleans the teeth, not the toothpaste. Stick with unfloridated until the aversion to spitting passes, and make sure she sees you and Daddy and big sister brush and spit, to imitate it.
I have the opposite problem, my 2 year old spits out the toothpaste before she has even brushed at all - she enjoys spitting right now, and she wants to spit everywhere, not just in the sink after brushing - the living room, the kitchen, the dinner table....so count your blessings! LOL!
Good Luck
Jessie