Should I let go of my ex-girlfriend?

Me and my ex went out for 2 years. We'd always have this fight and then we'd break up

and we'd get back together again, we've been doing it for 2 years now.

We got into another fight, and I broke up with her about a month ago.

I later then wanted her back, then she doesn't want to.

It seems there's a guy who is flirting with her, and she seems to like the guy.

Her family likes the guy too, while her family hates me.

She still likes me, and she still have feelings for me.

I love her so much. It's been a whole month, I've been desperately trying to get her back,

despite being hurt from her liking somebody else.

Her sister got into an argument with me and told me to just back off.

It seems that my ex-girlfriend will accept that guy in going out.

But I don't want to, I've been preventing it, but now, I just can't stop her.

I decided to let her have her way, and just wait for her if she needs me..

..but I don't really know.

Should I let go of her and move on? or should I wait for her if there is a chance she would come back to me?