How do you use the words their there and they're in a sentence about food?

First, remember when using a pronoun, you must be referring back to a noun in that sentence or the previous sentence, and there must be no 'noun-pronoun confusion'.

They brought their own food, but instead of eating it, they're letting it spoil. (Needs a sentence before this for the noun.)

There the food sat, but the family disagrees so much they're tearing each other apart rather than tear into their barbeque chicken. (they're and their refers back to family)

They're over there at the playground with their children. (Needs a sentence before this for the noun.)

A proper two-sentence would be: I looked for the family. Then, I noticed they're over there at the playground with their children.