I am a long-term sufferer of UTIs. I used to get them ALL THE TIME.
Some hints, (1) have her drink cranberry juice. (2) Lots and lots of water. (3) this is a last resort, and check with a doc first, but you should check to see if it's safe to use uristat on a 3-year old. It's an over-the-counter, low dose Pyridium (I think that's spelled right) which is an analgesic for the urinary tract. It doesn't cure the infection, but it will make the pain, frequent, and uncontrolled urination stop.
Good luck!!