Only way to really repair wooden furniture is to disassemble it, clean all the old glue off and start over. Frustrating part is, early stages of wobble can be very difficult to take apart (some joints are still tight) but if you wait too long the joints get so loose you can't take up the slack. Injecting glue into joints with a syringe is a Band-Aid at best and makes proper disassembly later more difficult at worst. 

With something like your typical chair, they have tapered tenons which can be shortened to tighten up the fit. The result will be a slightly shorter chair, but usually not very noticeable. Another trick is to use toothpicks to take up slack. Use small bits of masking tape to label the joints as you disassemble. Scrape old glue off (I'm not a fan of sanding- easy to remove too much wood).

Gorilla glue is good stuff- not just for outdoor use. It has a good long open time and you don't have to be so careful about cleanup like you have to be with white or yellow glue. Wear rubber gloves, as the stuff will stain your skin (it will eventually wear off). Always do a dry fit before applying the glue so you know you have everything ready and will get a flat, square result. Nothing worse than fixing a loose wobbly chair only to wind up with a tight, wobbly chair! Apply glue to one surface and spritz some water on the mating surface. It will foam up a bit as it cures, but it's not really a gap filler. If you need that, then use epoxy.