When cleaning a dining set which sits on an area rug, I find it most convenient to clean the entire area, including the rug, at one time… as if it’s an island unto itself. It’s a bit simpler than the ‘hard floors throughout’ sequence which requires that you return later to vacuum and mop beneath the table.
To check the task off your list just follow these few steps:
De-Crumb and Move Chairs Before or after moving chairs off area rug, lift cushions; get in-between slats; reach under baby seats; quick-dust lower rungs, etc. (Since the chairs likely have no pads or protectors on bottom of legs, be sure not to scratch the hard floor when moving.)
De-Crumb Table Move all items off tabletop; dust/cobweb overhanging light fixture; brush crumbs off tabletop; brush crumbs out of floor crevices near table legs and under supports; dust table rungs.
Clean Tabletop If the tabletop is ‘everyday sturdy’, I spray a fine mist of mild cleaner; wait a moment; scrub with non-scratch pad; squeegee; then polish dry. If I’m not confident the surface is hearty enough for a bit of soapy wetness and mild scrubbing, I just wipe with a cloth dampened with safe cleaner… making sure to remove stubborn globs with plastic putty scraper or extra effort. Spot check table sides and legs. Return cleaned items (centerpiece, placemats, etc.) after table is dry.
Vacuum Area Rug Thoroughly vacuum beneath and around table, and beneath area rug edge when chair placement allows.
Clean and Return Chairs Spot-check chairs for smears as you return them; thoroughly scrub baby seats (parents will love you~ just be sure to clean tray in sanitary fashion), check to be sure there is nothing icky sticking to chair leg bottoms (usually only a problem with pet hair on hard-floor felt pad protectors… not generally used for chairs on carpet).