You need to understand that it is a big change for her also to have teenagers in her house after a long time..

Be patient.. Old people are very used to doing things a particular way and are not ready to change.. Change means insecurity to them and if you suggest something better they only become defensive..
Part of it is lack of understanding and part of it is resistance.. They struggle to keep things going as they used to before...

Do things her way that will certainly ease some of the tension and also tell her her way works better although you might be sure you are right..Since she has agreed to take care of you at her age...it would be good if you can see things from her point of view..

If she is not much of a talker then just make sure you do your chores around the house (acc to her standards) and keep to yourself...Better not to give your opinions when its not called for ..
Make your stay more memorable and don't treat it like a punishment..

Cheers