Pressured into triggering situations.

I have a very close family but they can't understand why I get anxious about some things or how bad it is. Some times I think they must believe my anxiety is just a little nervousness. I feel weak because my anxiety controls my life and so I don't try to explain it to them, but this leads to them trying to force me into situations I simply cannot stand. For instance I can go shopping when I'm with someone and I can go early when there is no one about, but I can't go in busy times unless I am forced, and then the after effects make me have to stay in my house for days. So anyway I keep getting forced into situations that I can't deal with because my family don't get how much they effect me. Today my mum asked me to go to the shop and get her somethings since she lives far from the shops and the closest one is a lot more expensive than the one by me. I am going to visit her later today so it seems like a reasonable request, except she knows I can't shop, it's one of the few things I told her about, but now shes put me in the position where I feel like I'm terrible and am letting her down if I don't go. Then to make things worse she goes and says " I thought you loved me" when I said I wouldn't go, it is a horrible thing to do as now I feel more guilty for not wanting to go. I have to travel today so it's not like I can go and then after spend a few hours crying on the floor, I have a long drive to do insted. Being pressured like this is impossible to deal with and I don't know what to do.