Dr Mom
I don't know you, so, please, don't be offended, but one of the first things I would be wondering is if there is some kind of abuse going on that you are not aware of. If not, and you are just dealing with bladder infections, the first place I would look is her diet. Is she drinking anything besides pure water and fresh juices? Milk, soda, coffee, etc.? If so, stop all of it! These are way too abrasive on all of the delicate tubing that makes up the urinary system.
You are correct - continuous anti-biotics is harmful in many ways. One of the ways it is harmful you are already discovering - it tends to make super bugs which are very difficult to destroy, so the infections keep coming back and getting stronger because they are immune to the anti-biotics.
I have, personally, dealt with bladder infections a couple of different ways. Years ago, during one of my pregnancies, I had a bladder infection which I couldn't clear up. The doctor put me on several rounds of anti-biotics (this was before I knew what I know now) and then, finally, gave up and said I would just have to live with it - he said sometimes this happens during pregnancy. Fortunately, a friend, who lived out in the country, told me I could cure it by taking 4 or 5 alfalfa capsules 4 times per day and drinking lots of cranberry juice. I followed her advise and cleared up the infection.
In my midwife practice, I always advised women to take 2 kidney bladder formula with 1 cranactin four times per day and to drink 3 to 4 qts of water to flush it out. In severe cases, I would also add the infection formula. The herbs in the kidney/bladder formula tend to kill the infection - the cranactin keeps it from adhering to the bladder wall and the fluid intake flushes it out. The only time I have seen this not work was when a women tried taking the herbs with her Dr Pepper!?!
I realize you would have to adjust these amounts for a child and possibly use a tea or tincture instead of a capsule, but, hopefully, this will help give you some ideas.