lilblu, unless your grandma is usually a toxic person, i think you need to take a deep breath, and cut her a little slack. (I'll get to the cousin in a minute).
She is currently, if i understand, taking care of a disabled person. that is *very* difficult to do - it means that you lose your own freedom, your own *life*, and you are constantly dealing with *another person's problems*. it's not an easy thing to do - and when it goes on for a long time, it can become difficult for the caregiver.
Now she has a medical issue of her own. I don't know if it is something simple like an ingrown toe nail or somethign more complex and scary, but - she needed a hand.
and maybe she did take advantage of the fact that she *could* do a little extra shopping - but really, you are talking about an extra 45 minutes here. when an elderly person has to run a few errands (and maybe catch her breath), do you really want to be sitting there with a stop watch when they run a little over time? and she *told* you that they could call someone if you want - if you *really* couldn't/didn't want to sit there any longer, you should have told her to do that.
I think you should think about this from her point of view. If you can't do this and help her, then don't do it. but if you can - then maybe stop timing her outings, and maybe even start offering her to sit with granpa once a week or twice a month - yes, so she can go shopping or have a cup of coffee without worrying.
as for your cousin - simply say no. say that you are happy to sit with granpa but you cannot babysit anymore.