Yes they are, very common. Often with none of the symptoms that are typical of UTIs but with a massive downturn in the dementia symptoms. I think the primary reason is probably hygiene: that is, the person may not "wipe" appropriately or possibly at all. Apart from a bidet, someone helping them (and that's problematic unless they are late stage) or flushable wet wipes (1) are they truly flushable and 2) will they actually get used) there aren't many options. Using the loo is an intensely personal affair and most people will resist any help or even supervision. You could try giving cranberry juice (or cranberry capsules) to try to head these things off, but my sense is that while they might help if hygiene is OK, they are a drop in the bucket when they aren't.
Re the antibiotics: have you told the doctor how they make your mother feel? Because 1) there are other ABs that could be tried and 2) assorted things that might ameliorate the side effects. For example, if the symptoms are an upset stomach, acidophilus can help, as can making sure the ABs are taken as prescribed: some say after food, some say on an empty stomach.