At 18 months. I think it is a power struggle. Especially with girls. I say this b/c I am experienceing the same thing with my daughter. She wants to 'brush' her teeth on her own, and she actually does a pretty good job, no chewing on the toothbrush or simply swallowing the paste, and she has a decent grasp of the brushing motion, but there are still some times when she refuses to even brush her own teeth, let alone let me in there to clean up afterwards. I have noticed a difference in her reaction if I am using the 'adult' toothpaste or a toddler toothpaste. She definitely prefers the bubble gum and fruity flavors of the toddler toothpaste. Sometimes though, it simply comes down to me holding her down in my lap, and squeezing her cheeks together like she has something in her mouth I need to get out, this pops her lips open and I can at least get the front and side surfaces. I did not experience this issue with my 5 and 6 year old, and in fact they love brushing their teeth so much that I have to hide the toothbrushes and toothpast from them during the day. But they are boys, and their idea of teeth brushing is not as thorough as even my 20 month old dauther on her own.
All in all, I wouldn't worry about it too much. I have heard that the average mother only brushes her toddler's teeth about once a week in reality. So chances are what you are doing is fine for cleaning her teeth, and I would just be consistent in what you are doing and wait for her to move on to a new power struggle.