MissAdventure - I'm a long-time lurker on Gransnet but don't think I've actually posted a comment before. I understand you were open to all opinions but I do think some people are so self-righteous and haven't read the thread before posting.
My youngest DD is in year 11 (only just 15, so one of youngest in her year). In the October half-term 2019, when she was 13, my DH and I had planned a trip to the Caribbean to celebrate our 25th Wedding Anniversary. I am disabled and my youngest DD is a Young Carer. One of my other DD wanted to come away with us (paying for herself) and, because we hadn't had a holiday for a few years, we decided that all four of us would go away. I wrote to the Head of Year and explained the circumstances and requested that, as the school half-term was one week and two days, we could take DD out of school for the additional 3 days. This was granted and we were not fined. I believe it was listed as authorised absence.
I do understand that schools and teachers are up against it; however, it certainly sounds like your DGS would benefit more from spending time with his DB. I think you have done everything right - better to ask the school, rather than lie. You stated in a previous post that your DGS has 100% attendance for the past 2 years. I know of children who have time off sick frequently; in fact someone I know had to provide doctor's letters if her DS was off sick prior to Covid, due to the amount of time he was off sick with minor issues such as coughs and colds. I think schools consider a child's education is impacted when attendance is less than 96% - so your grandson is unlikely to be adversely affected.
Some teachers (including retired teachers judging by some of these comments) have a chip on their shoulder because they can't just take a week's holiday when it suits them - unfortunately, that is par for the course in the profession they have chosen, just as nurses and doctors and others in the emergency services have to work at Christmas. The poster who felt that children should be doing more work - they are children for goodness sake, let them enjoy life whilst they can - they are at work for many years when they are limited to the amount of holiday they can take.
I really hope your DGS has a fantastic break with his DB and that you are able to recuperate during this time, so that you feel refreshed on his return.