Training wheels do not help keep balance. Their primary purpose is to get a child used to the rest of a bike's features (pedaling, braking, etc.) while not worrying about the hardest part (balance). They can be used in a 'up' mode to 'catch' children when they overbalance one way or the other, but I haven't seen that be very effective in children I've seen learning.
I do recommend balance bikes (or removing the pedals), as recommended in the other answer. However, if you're already to this point, I suspect you can work with her directly.
The key is to not support her while she is pedaling/etc. Instead, give her a start, and then let her go, pedalling however far she can. Then repeat. With my children I would do this and count sidewalk squares; one per meter, roughly. This didn't take too long - a few days per child - but both had at least a little experience on a balance bike (I taught my older at 5 and my younger at 4, the latter had a year's experience while the former had a few months).
If pedalling is part of her issue, then I would definitely try a month or two on a balance bike or just removing the pedals and lowering the seat so she can have her feet flat on the floor. If she's a strong pedaller, then perhaps that's not necessary and you can just work on this. But the key is not to support her during the pedalling - just support her for a start.
I would also not hold her on one side. Hold the back of the bike if there's a handle there (there often is), if there's not then you might be able to hold the front of the bike (but avoid holding the handlebars if you at all can). It's important that you not add to her balance issues, and holding on to one side but not the other does create a balance issue.
Otherwise - just give it time, learning to ride a bike takes a while for some kids depending on their strength. Patience, and perhaps some pads and gloves (if the falls bother her), help tons.