get up (one's) nerve (to do something) - To muster or draw upon one's courage or resolve to do something. The Free Dictionary
In your context, the mother doesn't have the courage to tell her children what is on her mind (presumably because it's bad and she doesn't want to upset/disturb their play).
Fairly common idiom (at least in BrE).
Edit to answer questions in the comment:
For instance, let's say a teacher who is in a bad mood and cannot teach because he/she cannot endure dealing with kids for now. It has happened because they are not patient enough to do such that thing at that moment perhaps due to an unpleasant thing that just happened to him/her and they have just got to know it through a phone call. So, how would you explain such a situation when he/she doesn't have enough patience (as well as being nervous) to do it ?
The definition given about phrase as a whole. If we swap "Get up" to "Get on" we get a different meaning:
"Get on [ones] nerves" - To annoy someone a lot Cambridge Dictionary Def.
The kids were getting on the teachers nerves.
It's worth noting that the teacher is unlikely to have lost patience and be nervous, since those two traits aren't often seen together. You could say something along the lines of:
The kids were getting on the teachers nerves, but she was also too nervous to tell them to be quiet.