so is she not going cause it hurts her?? if that is the case you need to tackle that, because the trickling and not going properly and holding it will put her at a high risk of an infection.
things that MIGHT help (i have no personal experience though as my daughter is only 4 1/2 months old), give her cranberry juice to drink (even watered down) this will help her urine tract if an infection happens and might help prevent one.
can you get ural for kids? its a powder you add to water that you drink that will make the wee less acidic and not sting as much when she goes.
another option is when she goes pour water over her so it dilutes the wee and stops it stinging. I'm not sure how this will really work for a 2 year old though...
then, once you have it so it doesnt hurt to go, you can then tackle the using the seat again (having her not afraid of it). but atm she will just know that no matter what it hurts to wee. even if she is back in nappies if it hurts they wont help her (may even make it worse if the wee is sitting on her cut.

if i am way off and that isn't the problem, feel free to ignore this whole post =)