Libero switches
 

Is it legal according to high school rules to have the libero enter for the middle hitter then for the outside hitter, then one rotation for the second middle hitter? The libero would sit out one play while the second outside hitter serves and the libero would serve for the first middle hitter.

Provided there is one rally in between replacements (unless the libero is the next legal server), then the libero may replace *any* back row player. The libero is not limited in the players she can replace as long as that player is in the back row.

Libero switches
 

So the libero would need to sit out one rally after she replaces the outside hitter, before she could go back in for the middle hitter?

If so, this would result in her having to sit out two rallies in a full rotation of players. Am I understanding this correctly?

Yes, unless one is the next legal server, in which case she wouldn't have to sit out a rally.