Normally it's the person with dementia refusing, and often you can trick them into going, but if the main carer is refusing, even if that's a bad idea, I don't think there is much you can do apart from helping them in other ways with their caring role. I was awarded three weeks a year of respite for my OH but I very rarely used it as I couldn't find a care home I was happy with. That was my decision and as the main carer I think I was entitled to make it, as the consequences were for myself only.