I am not close to my mum but am close to my dad, he calls me every couple of days. But what we have, that my mum and I don't, is honesty. I am honest if I can't speak or see him cause I don't feel well or just simply not in the mood to talk. Maybe you need to let them know you're not feeling it right now and not coping. Sounds like too much effort to see them this Saturday to me. Don't make yourself feel worse, there is no harm in putting it off for a little while.

I know it may be hard to be upfront with how you feel but I started doing this with my dad and our relationship has improved tenfold.

Wishing you the best!