I find the fact that Peridot probably had a stark realization that she and the others are basically living in someone else's dream pretty emotionally powerful. Life on homeworld wasn't as it seemed, the diamonds are actually cruel and unforgiving. Everything was really a mess and she like millions of others were brought up to believe otherwise. I think this is when she finally realized that this is what she wants, to be free, and live her own dream. She doesn't want anyone to ruin that.
Peridot had to cope with the fact that everything she believed was wrong. Her entire view on her home, her Homeworld peers, her idols, and how order really should work have been completely thrown out the window. She probably had to feel lost and alone, as she is the first homeworld gem to actually join after the rebellion. She began to love Earth and free life through experiencing it, a privilege most crystal gems did not get to have.
And now that she and Lapis both are living happily on Earth, she was there for Lapis, helping her adjust. Lapis had a different situation though. She had no side, and she kept her past views on Homeworld. Lapis, although needing to get used to a few things again, seems contempt with everything. So not only does Peridot have to manage an entirely new belief in how life works, she must go about it herself. Noone can truly understand how she feels about that, but it doesn't mean others aren't there to support and love her.
