This is Sam's war to fight, and not your own. I realize you care and you want to be supportive, and also that it's affecting you.
But you're not being affected like she is. So take your cues from her, rather than trying to find solutions for her (unless she specifically asks that you do just that).
As for you and her mom, well, you wouldn't be the first-ever gf or even spouse where a parent pulled an ultimatum out of their ass and yelled, "If she's going, then I'm not!" So go where you want to go, long as Sam is okay with it. Don't walk on eggshells around Sam's mom. Live your life.
Sam's mom is passive-aggressive at the best of times, and homophobic at the worst. And I'm sorry. Will she ever change? I have my doubts, but people sometimes surprise us.
But either way, take your cues from Sam