Learn Dutch: We moeten morgen op ons kleinkind oppassen. - We have to babysit our grandchild tomorrow.

The verb oppassen (to babysit or watch) is paired with the fixed preposition op when you specify who or what you are watching over. It works a bit like saying to keep an eye on in English.

Why is it ons kleinkind and not onze kleinkind?

The noun kind (and therefore the compound word kleinkind) is a het word. For singular het words, the Dutch word for our is ons. You only use onze for de words and all plural nouns.

Oppassen is a separable verb, so why isn't it split up here?

You are right that oppassen is separable (op + passen), but in this sentence, it is paired with the modal verb moeten (have to). The modal verb takes the second position, pushing the main verb to the very end of the clause in its full, unsplit infinitive form.

If I take out moeten, how does the sentence change?

If you remove moeten, oppassen becomes the main conjugated verb and has to split. The sentence would become: We passen morgen op ons kleinkind op. Notice how the prefix op goes to the very end, while the preposition op stays right in front of ons kleinkind.