I have twin brothers who struggled for years with saying their R's. It was getting worse, and becoming very frustrating for them, as they had no other problems. When they finally went in to have it looked at, turns out they were tongue-tied (just like your daughter, though not as much as her). Here are the basics:
The skin below the tongue is sometimes too tight, or extends too far along the bottom of the tongue. When this happens, the tongues is physically incapable of moving certain ways to make certain sounds; no amount of therapy can change this. The tongue is tied down.
All my brothers did was go in to the doctor, and he used a laser to clip the extra skin. Their tongues were hardly sore, and after the first day there was no pain whatsoever. Now they can say their R's just fine, and are very, very happy.
Clipping the tongue does not mean cutting her tongue away from her mouth. The extra skin/taut skin is only clipped back to the point of a normal, un-tied tongue. No more. This gives the tongue the mobility to move as it should.
Think about this: if someone is hurt, and they end up with extra scar tissue that inhibits their ability to move, the logical thing would be to surgically correct it so that they would have natural mobility returned to them. This is a simple thing to correct, and I promise you, the doctor will not be doing anything barbaric to your daughter's mouth.
Your daughter is not disabled; she has skin that is too tight or that grew too far along the underside of her tongue. If she has the procedure, she will talk as well as anyone.
I would advise you to go ahead and have the procedure. It will save your daughter a year of frustration, and you time and expense.
Go with the laser procedure, too. She might be a little sore the first day, but nothing more. The pain is minimal with a laser, and the healing is super, super fast.
I hope this eases and calms your mind. My brothers were thrilled to have it done, and highly recommend it.