"My children are playing with their friends over in the swimming pool."
Translation:Tá mo pháistí ag imirt lena gcairde thall sa linn snámha.
clann is a singular noun denoting a set of descendants, it's not really a group noun denoting a collection of individuals.
It's unlikely that you would interpret "my children" in this exercise as meaning your children as a group, rather than that they are each playing as individuals, so mo chlann isn't an accurate translation.
In Chuaigh mé suas le mo chlann agus mo chairde you are referring to two distinct groups - "my children" and "my friends". You can simply replace "my children" with "my family" without altering the logic of the sentence.
In this exercise to change "my children" to "my family" would imply that your children are acting as a group with a single purpose, whereas children playing with their friends in a pool are each likely to be acting as individuals, not as a group.
You would be understood if you said mo chlann but there is a distinction between mo chlann and mo pháistí that you might be missing if think that the two phrases are synonyms.