Two weeks is a really long visit! You absolutely have to schedule time to see other people and do things on your own. That will make the time you do spend with your mother a lot better for both of you, whether she realizes it or not.

One thing that might be effective with your mother is not telling her about your plans to visit friends until you are leaving to see them. Then you won't have to listen to her moaning about you going for two days beforehand. If she gives you the silent treatment afterwards, you could tell her 'Since you seem like you want to be left alone, I'm going to go shopping,' and just leave.

Keep reminding yourself that you are not the one who is being unreasonable. If it's easier to just give in for the two weeks, that's fine too - but if you don't want to, you don't have to. I don't think she is going to change at 82, but you can still change how you interact with her.