No advice, though I hear similar from my mum who is about an hour away, and who also turned down the opportunity to be in the childcare roster (I also work 4 days,DD now 3.5 is in term time nursery but at the start we had a nanny so my mum could have done a day a month or a day a fortnight and we'd have scheduled the nanny around her).
I get childcare is work, but honestly if they are close enough and declined to help out, I have limited sympathy.
I don't see my mum as often as you, but it's easily once a month, sometime just us, sometime confined with my siblings and their kids. She comes here more often.
She means both about frequency and about us not going to her more. What she'd really like is more frequent visits (and more to her) without her having to do much.
I ignore her. We have busy lives and I'm clear that if she isn't going to be helpful, I'm not giving up more of our time to facilitate her seeing DD when she's not prepared to make more effort.
Now DD is in a school hours term time nursery we have found a good format where she visits during the week, does some pick ups and drop off. That helps us out if our nanny is off and is manageable for her: she finds the idea of full days with DD a bit much (though it generally goes well if she does it).
So I continue to look for more opportunities for contact, but only if they work for us.
Think gps need to own their choices. Not doing childcare is a totally fair enough. But then you have to understand you are one of many demands on free time and there are other things to be factored in: family time, free time, other gps, seeing friends etc.
Vice versa if you do do some regular childcare you have a direct relationship with the gcs, which makes it easy to slot in. You put more in, you get more out.
I've written myself a letter to remind myself of all this when I'm the gp!