wow, okay...

I always try to avoid chemical drain openers, because they often don't work and make the problem worse by somewhat "melting" the clog... just enough to really clog things up. Not to mention can damage pipes and fixtures (and tubs). I wouldn't let the plumber off the hook for the damage done to your tub -- and I'd get a different plumber.

That said, two things can be very effective:

1. a plunger used to "suck" the clog. Partially fill the tub (or sink) with water. Collapse the plunger to get the air out of it and then seal it over the drain. Pull up on the plunger (hard and sometimes up and down a bit). the idea is that you are pulling water backwards through the drain and this will often open it. Repeat this several times. You may have to cover the overflow with a wet rag to seal it.

2. electric snake - which you've tried.

Some older plumbing used a drum trap for the bathtub - it was typically so you could access the trap from the same floor as the tub. These type of traps are impossible to snake and have to be opened to be cleaned.