Scarlett is correct - you need to use Past Simple:
When I WAS a kid, my mother TOOK me to the park where I PLAYED with the other kids.
When I was a kid, my mother took me to the park TO PLAY with the other kids. (for that purpose)
We often (but not only) use Past Continuous when an action has been interrupted:
I was playing with the other children when a dog ran across the playground.