Dining chair refurbish, what glue to use?

If the joint is tight fitting, then a wood glue will do ok. Something like Titebond III retains slightly more elasticity when set than the more traditional PVAs - although its slower curing that say Titebond original. For loose fitting joints or where set time is critical, then 5 minute epoxy.

I used Cascamite, but I was willing to wait!

If the chairs actually wobble the wood has probably dried out so any glue is going to crack again. I'm sure there used to be something that expanded a bit after it was assembled but I've forgotten it now. Brian

Just done four dining chairs from the in-laws with loose backs and legs. Joints fairly tight but not tight enough to stop a wobble. I just used PVA wood glue. Did a couple here the same way a few years ago, still solid.

Not sure that a glue that sets quickly is a good idea witha complex structure like a chair. Something may fit well together but not quite in the right place when fitted to the rest of the chair. Being able to assemble and get everything into the right place for the whole is what you want.

Doesn't Gorrila Glue foam up?

It does, but the foam has no gap filling strength. If you need gap filling then epoxy (with added filler if required) is the usual way to go).