Am I right to be upset about my manager texting me when I’m off the clock?

You have a right to say no once in a while, but what you said was inappropriate and unprofessional. All you had to say was no I can't come in this time, maybe next time. She will move onto who ever else is available. 

If you don't want to work on weekends, turn your phone to silent mode. Don't answer if she texts you. 

She's a manager and probably has some experience being one, so she's going to get payed more then you. If she needs help she's going to text you, because she knows you won't turn her down. 

Your reply was inappropriate.  If you didn't want to work that evening, a simple reply of, "Sorry, I'm not available tonight," would have sufficed. 

As mentioned in the other responses, you need to give some thought to your attitudes about work.  It is important to set reasonable limits on how much extra time at work you will put in.  Your attitude toward work in general, however, is very bad.  "She needs to fix whatever problem...,the other stupid employees...that's not my role," are all glaring red flags.  

You aren't worth anything more than minimum wage, if that. Your behavior was a disgrace.  No, it was not ok to tell her that.  And she was trying to fix the problem - she called you.  I don't think you are ever going to make anything more than minimum wage.  Not unless you change your whining, complaining, entitled attitude - to start.

You can tell her "no".

She will start offering other employees instead of you opportunities.

Thank goodness Y!A is going away so we don't have to hear about how you are stuck in a dead end job and don't get raises.