She probably did try and find someone to watch her child. There is no way for certain for you to say or think she didnt. And maybe her child is really sick, and maybe when the child is sick she prefers her mother, which they generally do. Its understandable. And I honestly wouldnt want to leave my child while he was sick anyways.
It's ONE meeting, and sorry to say, she is a mother FIRST and a GS leader SECOND. If my child was sick then I would stay home with him too and not hold the meeting. I would hope the other mothers would have enough compassion to understand that and either A: let someone else do it, or B: not hold it that night and reschedule for a different night.
Also, maybe she has reasons to not let you hold the meeting. Its a possibility. Whether they are personal reasons or whether she just feels that you have too much on your plate to stand in for her. You have said repeatedly that you are a full time nurse, pregnant, and school etc she probably figures you would either be too tired or too busy. Either way its her choice.
Its just one meeting, so just enjoy being home, relax, and not worry about it.