These sentences all have various problems that you introduced by using various tenses. Also, it's not usual to say "the mom", but instead user her name or explain her relation to the subject of the paragraph/story, i.e. "Mrs. Raccoon", "the son's mom", "his mom" etc.
[Mrs. Raccoon] had prepared some food for her son before he left.
When you say she "had prepared", it requires that some other significant action happens afterward; however, here, nothing happens. "Before he left" is an adverbial phrase that only tells us when the action happened, and doesn't really justify the past perfect tense. Instead it's better to stick to the simple past, "Mrs. Raccoon prepared some food for her son before he left (for school)."
Mrs. Raccoon had prepared some food for her son before he was going to leave.
Again, "had prepared" is not justified, but on top of that, "before he was going to leave" is odd here, possibly because it represents a potential future action, and the mother's action (preparing food) is definite. So there's a weird mix of verb tenses that don't agree with each other. Instead, if you really have to, you could say something like, "Mrs. Raccoon would prepare food for her son before he would leave (for school)," or better, "Mrs. Raccoon would prepare food for her son before he left (for school)," or even, "Mrs. Raccoon was going to prepare food for her son before he left (for school), (but then Mrs. Fox came calling and she completely forgot)."
Mrs. Raccoon had prepared some food for her son before leaving.
This one is actually better than the others, although here it's Mrs. Raccoon who is doing the leaving. "Leaving" by itself isn't wrong but still feels incomplete, "Mrs Raccoon had prepared some food for her son before leaving (to go visit Mrs. Fox)."
That girl who had meetings the next day would eat some food first.
This seems needlessly complicated. A simpler sentence would be, "If she had meetings the next day, she would first eat something."
I understand that you might want to use a certain grammar ("the [subject] [defined by some condition] would do [some action]"), but while it's not necessarily incorrect it can be hard to understand. The problem in this case is that the adjectival clause doesn't just define who we are talking about, it also explains the reason for the action. It's better to group together the action and the reason, so their relationship is clear, "That girl would eat some food before she went to her meetings," or, "That girl would eat something before she would go to any of her meetings."
There's also some confusion about time. When did she eat? Now, or before her meetings the following day? A (relative) future plan has to use some kind of future tense, otherwise it sounds odd. "She had meetings the following day, so she planned to eat something before attending them."
