Shaker Table Shaking

I wonder if this table can be restored by someone like myself, who has little knowledge of woodworking and no lathe for slow sanding of table legs as mentioned on another thread here?

This table has had a sticky backed topping taken off and needs to be sanded right back. The big problem is that the two back legs have been forced out of their joints, and then someone has tried to nail them back again. This has made cracks in the tops of the legs, and I need to remove the nails without further cracking. I'm thinking of Dremel tooling around the nail heads to to present them better for gripping. If I am successful at removing the legs without too much further damage, what glues and paint strippers are best for this job please?

My main tools are a GMC scrollsaw and a Dremel tool, which will give some idea of the equipment I have.

Buzza.

"all my heroes drink beer because they can't spell cognac" wc fields ...