Thank you for all the replies.
I will try and answer the main questions.
WFH parent is a good parent, hard working, hands on etc. so I do feel like they are getting a bit of a pasting on here based on this one situation, which wasn't my intention.
WFH parent is quite intolerant to noise/distractions generally, something they struggle with and they do a very technical job which requires a lot of concentration. They have definitely found having children challenging for this reason...
WFH parent cannot go into the office easily, doesn't have a permanent desk there, and working from another space would be tricky due to technical nature of the job and electronic equipment required to work effectively. They do have an office at home, but it's small and off of the main hall, so it is quite noisy. However there is no other space for a home office in the house.
Other parent/GPs could definitely make more of an effort to stop children causing a disruption to WFH parent, so this is something we will work on. However it IS a home first, as some posters have mentioned, so I do think balance is required.
Children doing an overnight with GPs is probably not an option. GPs never expressed any interest in having children over night, but are happy to look after them for a day here and there. And there is no "expectation" of childcare - they have said they are happy to look after the children sometimes to help out and we're welcome to ask if needed. They have said no on many occasions when not convenient for them. Fine.
GPs don't mind if they have children at their house, or look after them at our house. But they are not prepared to do 4 x 40 minute journeys, which I think is a perfectly reasonable position. Unlike WFH parent who seems to think that would be a reasonable expectation of GPs. I do not agree it is reasonable in the slightest, hence this post!
Cheaper holiday clubs don't exist around here. If you want childcare for most of/all of the working day then you will pay £40-50 per child. But that is fine, they are our children and if needed, and another compromise cannot be reached in terms of expectations of GPs and WFH parent, we will pay for more days of holiday clubs going forwards.
WFH parent likes my parents... but also finds them frustrating in many ways (they are very different to his parents and can be quite frustrating at times to be fair!). But there is a resentment there that they don't want to do more with the children (e.g. have them over night for sleep overs). My parents love the children, but also could probably happily live without seeing them much, they have busy lives. They also expect the children to be able to entertain themselves in certain situations, i.e. when we all meet up and adults are talking, my parents would much rather sit and have an adult conversation than be running around with the children. Whereas his parents spend all their time actively playing with and entertaining the children. I personally agree with my parents and think the children should be able to entertain themselves sometimes, but there's a mismatch between the two GPs and of WFH parents expectations as a result I think...
I don't know if that covers all the main questions asked... but there you go. I think that's most of it.
In summary expecting GPs to do +2.5hrs travel in a day to collect and drop children is unreasonable, and we need to look at alternative options going forward that work for everyone... possibly not involving GPs at all.