How do I get her to commit to me?

[Joe]

even if you could convince her to commit again, it doesn't sound like this relationship is ever going to last long term

you had one year together that was good, a lot of relationships are awesome for a year

after she went 2 hours away, long distance relationships never really work out well. she was probably cheating longer than you knew, that's what happens like 90% of the time with ld

you're only making it harder by trying to be friends and keep getting together and breaking up again

If you want her that much this is probably what you'll have to deal with,
but I'd say move on, it's not happening