Learn Hardcore Dutch: De kinderen rollen de bal door het park. - The children roll the ball through the park.

In Dutch present tense, plural subjects always take the infinitive form of the verb (the -en ending). Only third-person singular adds -t (hij/zij/het rolt). So you say:
• wij rollen
• jullie rollen
• zij rollen

Why is it de kinderen but het park?

Dutch nouns are either common gender (use de) or neuter (use het).
• kind(er) is a common-gender noun → de kinderen
• park is neuter → het park
Unfortunately you must often memorize which nouns take which article.

Why is the plural of kind kinderen and not kinds?

Most Dutch nouns form the plural with just -en (kind → kinden is actually old-fashioned). Some, like kind, use an irregular plural: you add -er plus -en → kind + er + en = kinderen.

Why does de bal come right after rollen, and why is door het park at the end?

Dutch follows a Subject–Verb–Object–Adverbial (S–V–O–A) order in main clauses:

De kinderen (subject)
rollen (verb in second position)
de bal (direct object)
door het park (prepositional phrase/adverbial)

What does the preposition door express here?

Here door means “through,” indicating movement from one side to the other inside something (the park). It’s equivalent to English through.

Can I use doorheen instead of door?

Yes. doorheen also means “through” and can feel a bit more colloquial or emphatic, but in everyday speech door is shorter and more common:
• door het park
• doorheen het park

Why doesn’t Dutch show a continuous tense like English “are rolling”?

Dutch doesn’t have a dedicated continuous aspect. The simple present (rollen) covers both habitual and ongoing actions. If you really want to stress “right now they’re rolling,” you can use aan het + infinitive:
De kinderen zijn de bal door het park aan het rollen.

Is there a separable verb doorrollen, and would that work here?

There is a separable verb doorrollen, but it means “to keep rolling” or “to roll on” (e.g. de bal rolt door = the ball keeps rolling). It does not mean “to roll something through” – for that you need the verb rollen plus the preposition door.