I've had RA since age 5 and am now 50. The only time I've taken opiates is post surgery, never to manage arthritis pain. However I know others who do take opiates, so you won't get any judgment from me! :)
Keep in mind your blood tests may not show anything definitive. Many of us with all the classic symptoms never show a positive Rh factor or high sed rate in our blood work, or it shows up much later. But hopefully your rheumatologist will go ahead and treat the symptoms you present.
It can take time and patience to find the right combination of medications for you. There is no "one size fits all", unfortunately. Hang in there, and perhaps ask for a referral to a pain management specialist.
Even if you are flaring (the disease can come and go in flares, or be more of a chronic condition), it's important to keep your joints moving. Gentle exercise is essential - walking, swimming, cycling, anything non-impact. It might hurt a bit, but the general rule of thumb is that if the pain subsides after a few hours of rest, you're okay. If it still hurts the next day, you did too much and you need to ease up.
Coaching? Sure, why not? Running up and down the field with the kids...hmm, that's a tough one. You may need to have an assistant coach help you out, or have some of your more talented players do the more strenuous demonstrations that you're trying to teach your less experienced players. Then again, once your symptoms are managed, you may not have any problem at all.
As for tae kwon do, that one's tougher. You'll have to consult with your rheumatologist on that one. I'd be careful of anything that's high impact. You could definitely do something like tai chi, or other types of martial arts that require forms. But I'm not certain about the high-contact sparring part.
Hang in there! Hopefully once you find the right combination of meds, flares won't be as severe and not as much of an issue for you. Good luck!