Tending to children's needs during family gatherings (e.g. preparing their meal and making sure they are fed, putting them to sleep, putting sunscreen on them, changing baby's nappies). Is it OK for GP to take on some of these tasks or can that be perceived as interferring?
I love passing this stuff on to willing GPs. They can change as many nappies as they want! Obvious caveat here is that I trust my DDs' grandparents so if they have helped with sun cream, or made a meal, I'm comfortable that what they've done will be fine.
Holding babies and physical affection with children. How much is too much?
I have a baby and a toddler and as long as they are happy, GPs can hold/cuddle as much as they like. They always pass them back when asked.
Calling to "request" family time - suggesting they visit for holidays, weekends. Organising meetings so that they also visit extended family. Visiting to take children to the park/ cinema
Depends how often. If they called every weekend then it's a bit much. But wanting to see grandchildren regularly, or take them to the playground sometimes is fine with me. As for extended family, with my PILs, their parents sometimes come to stay with them, so yes, visits with DDs' great grandparents are arranged through MIL/FIL and they will say to DH "grandma and grandad are coming to visit, they'd like to see DDs". I'm fine with this.
Calling/ texting to check how doctor appointments/school functions/other events went
If I've told them about the event, I'm happy for them to ask about it.