Thank you for writing. It won’t help to make this an argument about who is right or wrong. People generally don’t stay open to ideas if they feel that talking will result in a fight.
What will be more helpful is to approach your parents with your confusion (not your anger or frustration) about why they think working in your former community is a poor choice. I do have a couple of guesses: They may not want to “burden” their friends or seem to be taking advantage of the friendship. Or they may want you to adjust to your new community and find friends there. Often a summer job is where teens connect and make new friendships.
I suggest that you try asking them. Stay calm. Stay open to their concerns. Politely offer your point of view. It sounds like you have the kind of positive relationship that a teen needs to have a positive and rational discussion.
I wish you well.