Welcome to the site!
If your goal is to make this case of tendonitis last all year, go ahead and let the coach rush your kid back into action every time the symptoms ease a little bit.
We had an excellent trainer at our high school. Two things he said made particular sense in situations like this:
1) Never predict a player's return to action more than 24 hours in advance. Even if you know the normal course of recovery for a given injury, you never know how the recovery will proceed in any individual case. Just keep following the program laid out by the physical therapist or other competent person each day and don't try to guess at time lines.
2) When a player is injured, he doesn't play again until the doctor, the trainer, the coach, the player, and the parent all agree he's ready. Only the coach has the authority to put him back in, but each of the others holds veto authority.
Stand your ground.
Best wishes,