How can I decide when it would be correct to use the "new-parents" tag?
The parents tag has this description:
About the parents themselves, and not (only) about the children.
So when your question relates to parents more than to the child, use the tag.
The new-parents tag doesn't have a description and, in my mind, doesn't make a lot of sense. Either the topic relates to the parents (see above), or it relates to the child, in which case no "parent" tag should be applied but rather one of the age-bracket tags like infant, toddler, pre-schooler etc.
I think we should remove the new-parents tag.