Okay, before I get started I have a quick question, I noticed in one of your other posts you mentioned one of your girls has hypermobility syndrome, is this the same one with this wrist pain?
Just a few thoughts on the matter for you-
1. I will start by saying, don't use KT tape. As some have mentioned, if not used correctly, it can do more harm than good. I also wrote my final research paper on it in undergrad, and basically the research concludes that there is not enough evidence to prove its effectiveness, and for the price it goes for these days, I would rather stick with my white tape that I know does the trick.
2. That being said, you might not like this answer, but I also avoid taping altogether. Sure, I'll tape the kid that has an acute ankle sprain and is doing rehab with me while also trying to get back into the game. But chronic conditions? It's definitely a case by case scenario type thing. I don't like to consistently use it because kids tend to use it as a crutch, and to avoid treating the underlying cause. What we do as ATCs is just as much about the mental aspect as it is the physical, and I don't like my kids to get the notion in their heads that they NEED to get taped to play well. (again, some exceptions... try telling your varsity football coach that his starters don't need their wrists taped lol)
3. The underlying cause- in your daughter's case, tendinitis, is a chronic inflammatory condition. Prescribing her Naproxen is only going to help decrease the inflammation, which sounds like a good fix right? Yeah, until she goes to practice and flares it back up again. If something is chronically flaring up, that means there's something else going on as well. Whether it's weakness in structures, a change in the biomechanics of the joint, etc. So the best place to start? Strengthening around the joint. Often times people get the idea in their head that they only have to strengthen the part that hurts, IE- I sprained my ankle, so I only need to do ankle exercises. wrong. The whole body is a kinetic chain, so everything is essentially connected and can impact another joint. Wrist injuries are tricky to rehab sometimes just because of the nature of the joint. You're suppose to strengthen around, aka above and below, the joint, so in the wrist, that would be the hand and the forearm. Some of my wrist injuries I even include shoulder exercises depending on what the injury is. But you can only get so creative with exercises for the hand. What you need to do is strengthen your intrinsic muscles in the hand, the tiny tendons that run through them. Things you can do for this include getting a stress ball and squeezing it, or something like playdoh or silly putty, and have them work it over and over until their hand is sore. I think you can buy those grip masters as well at like dicks sporting goods or even honestly walmart. those can help as well. I've never seen the webs in stores, but if you have them, also worth investing in. As far as the forearm goes, you can start with some basic wrist extension/flexion, ulnar and radial deviation, forearm pronation/supination, and elbow flexion/extension exercises. Depending on her pain, you may be able to just have her start with active range of motion with it (doing it without any weight or resistance) and then progressing to bands or dumbbells. You will probably have better luck finding dumbbells in stores than bands. I tried to find some good videos on youtube to show you how to do them, but they are all like 8 minute videos full of crap you don't need. It's just kind of hard to put some of it into words. But basically you're trying to strengthen AND stretch all of those movements. don't underestimate the importance of stretching it out. Some people forget about those "less important" muscles... most cheerleaders are focused on the bigger picture that usually involves things related to heel stretches, scorpions, etc...
Sorry for the long winded message, I'm a nerd and I get excited to educate people on this stuff rather than just telling them what to do. I like to touch on the why. If you're confused about anything or still have more questions, feel free to PM me!
PS- just because this is the perfect time to throw it out there, this is just one more perfect example of why I want ATCs in cheer gyms. If there were, I wouldn't have to explain to a mom via a cheer board how to help take care of her athlete, I would be able to be there to take care of her, and potentially prevent the injury from happening in the first place. just some of me .02 cents for the day :)