Furniture & Upholstery Restoration Job - Herlear, NC, 8301

I have an old wooden chair, part of a dining set. It's wooden supports have come loose, so now the chair wobbles forwards and backwards. It seems as if it was glued into the chair legs, but I can't take it out to apply glue inside again, so looking for someone to fix it for me. It is an antique, belonged to my grandmother, so for great care to be taken please.