Controlling a friendship

Hi, my 13 year old daughter is on the outs with her best friend and and I’m friends with the mom who lives behind me. Even though I understand why my daughter doesn’t want to be friends with her anymore because she was getting very possessive and wanted my daughter to only hang out with her, I find myself constantly pushing for her to make up with this friend. It gets my daughter mad and she keeps saying well then you don’t understand how annoying she is and then she walks away. I guess it just makes things awkward for me them not being friends and I worry she won’t have enough friends and will be lonely. So I make comments I guess I shouldn’t. Any advice on how best to handle? I know at this age they are old enough to choose their friends.