Clear as mud. ;)

If your tile installer (c) works as an employee or sub under sub contractor (B) who in turn works under the direction of the GC (A) for the entire job, then no, you can't poach them from the sub or GC and hire them directly. Your money pays the GC (A), who in turn pays the sub (B) who pays his employee (C), the tile installer. You have a relationship with A only, and it's A's responsibility to deal with B&C, not you.

Now, because you have a GC on the job, you can hold his feet to the fire about your dissatisfaction with the work that any of the subs are providing. However, this is an issue that you address with the GC only and let HIM solve. You don't start talking with the subs directly, or give them direction, as that's when communication starts being an issue and you end up paying the price for that. If there are enough problems with a sub, the GC will end up changing subs. But, that's HIS problem to solve. You just need to get with your GC and register your issues, then ask him what he's going to do to solve those issues. That's a GC's role.

But, perhaps I am misunderstanding your narrative.

Talk to your kitchen contractor to see who you need to address issues with.

Live wire, thank you for putting into words what I was trying to say__you got it exactly right. Unfortunately, when I do contact the GC, he doesn't get back to me either. I don't feel as if I should have to chase the GC down. It seems to me he should be checking on us to make sure the kitchen is getting back together and he can get his final payment.