Has she been x-rayed yet? I am only suggesting an x-ray because that is how it was discovered that my 3 yr old girl Abby had bladder stones. She (Abby) had many of the symptoms that you are describing in your original post. Abby was previously "diagnosed" with a UTI in june and was put on two separate treatments of anti-biotics. as hindsight would have it, I now suspected that she possibly may have had her bladder stones back then.
In regards to getting a urine sample, Abbys' vetinarian squeezed (or compressed) her belly on the exam table, and she expressed out a puddle of urine, in which they sucked up with a syringe to test. Her PH level was way up too.

Her x-ray showed a bunch of stones in her bladder...looked sort of like a nest full of little eggs....around 10 stones were in there

She had surgery, to remove them, and is now on a prescription diet, and she is now back to going to the litterbox normally.

Here is my original thread on it:
http://petoftheday.com/talk/showthread.php?t=114745

here is the thread here on PT that shows her belly before and after surgery:
(pictures included)

http://petoftheday.com/talk/showthread.php?t=115310

Maybe this all will be of some help to you