So they 'don't have time', but expect you to keep going even though your situation has massively changed??
They're piss takers.
I'd set it out like this.
Depending on how much you want to share:
Dear unreasonable people,
I have been taking pooch to see your mother monthly for the last x years /months.
I can no longer do this (at all?) as my situation has changed in an unpredicted and life changing way. This is a permanent situation.
My child's medical needs HAVE to take priority for me.
As I saidn(on x date) I'm happy for you to take Fido to see your mum but I can no longer commit to these visits long term...
If you want me to continue I may be able to do this on an 8 weekly basis, and review this as time goes on.
The alternative if you're unable to take Fido to your mum, we arrange a goodbye visit.
If course we'll continue looking after Fido as per our original commitment. Let me know your preference.
..........
They'll probably argue /want you to justify but hold your boundaries.! (say repeatedly... 'it's all in my letter /nothing has changed /that is still my position).
Good luck