Thanks for all the help!
We watched them last night and they seemed to calm down a bit. I felt comfortable enough to leave them overnight. I'm at work right now but my grandfather has been watching them all day for me (they're in his office). He says that they are doing fine. I'll probably swing by and pick up a tank divider in case things go south again.
I did introduce the betta into the platy tank, just fyi. I had bought a new 10 gallon tank, put the platies in it, and then added mr. betta later on.
I had read that platies and bettas were fine in multiple posts on this forum so I figured they'd be alright.