FunkyMunkie,
This brings back memories of your babies when they were small. They were so tiny and just wouldn't "EAT ALONE", so we used to put them on our bed and bring their dish there too, so they would eat. This happened with both girls now, so I know what you are going thru. Instead of the threat of them going into hypoglycemia and shaking from lack of eating, we made sure they ate. IT wasn't a problem as we were spending time with them at meals.
NOW, I think they think its a "FAMILY DINING TIME" , my husband and I both line the bed with the girls for their meals. They "dine" only when one of us are with them, and sometimes they go and get the other parent so we can be a "FAMILY", its so funny to see.
YET, I worry, if anything ever happened to us, we had to let my daughters know of their habits so they will be able to carry on with them to eat.
We don't mind the " FAMILY DINING TIMES", they are so small and its too drafty near the floor for them, and definitely for us. Good Luck.