First, I would suggest you get a padded vinyl table cloth for use during the kids projects. No finish will hold up to that potential abuse.

I am assuming that your farm table is made of solid wood which can stand some really vigorous sanding. Take it down to bare wood and start over. Stain it to match the existing stain, or leave it natural. Natural gives less problems wtih possible future damage touch-ups.

Finish with at least 3 coats of urethane varnish. The varnish will probably need a light sanding after the first coat as the grain will likely lift slightly. The second coat will make it look good, and the 3rd coat gives the additional thickness to withstand future wear.