S.,
In my opinion. catheterizing a 2 year old to check on a run of the mill Urinary Tract Infection is a bit extreme....and I agree that it would be very traumatizing for her, unless they were to do it in the hospital with general anesthesia.
Another clean catch urine specimen, once she has finished her course of antibiotics, should tell them whether or not the infection is gone. If you were not able to collect a clean catch specimen from her the first time, the remedy for that is quite obvious... have the office nurse, or the doctor do it herself!
Although it pains me to say this, many doctors are more concerned with how many procedures they can bill you for, than they are with the welfare of the child, which may or may not be the case here. If the doctor is, indeed, suggesting this in order to charge you a greater amount of money for her treatment, then she is doing it at the expense of your child, which, in my opinion, is inexcusable. If she is not, then she should have no objection to having this test done in the hospital, where your child can be sedated.
I am, in no way, telling you what to do, but if she were my child, this procedure would be done while she was under sedation, and would have no memory of it, or it would not be done at all!
Also, just for your own information, if you are using any sort of bubble bath in the water when you bathe her, this is a leading cause of Urinary Tract Infections in small children, especially little girls, or if you are putting her in a pool of any sort, this could also be the source of the bacteria that may have caused the initial infection. If she spends time playing in a pool of any sort, then be sure to wash her private parts well with soap and water, and dry her well, before you dress her!
As far as reflux disease is concerned, I have no knowledge or experience with that, so perhaps that may be why they think that a catheterization is necessary, but, if so, the procedure could still be done in a hospital, under sedation, to make it easier on your child, and on you!