So, whilst you weren't being unreasonable not to take him out if you wanted it to just be you and your dd, your attitude towards your nephew and his parents is totally unreasonable.
I have a 16 year old ds. He has been refusing school for the last two years (year 10 and 11). I am educated to post grad degree level, as is my DH. My two daughters have both been in school fulltime (although the elder one has now left, having doner her A levels last summer and is planning to go to University next September). So I think you can see that we do, really value education.
My son hasn't been happy in school since about year 3 or 4, but he carried on going and even managed 100% attendance when he was in year 6. The transition to secondary school didn't work well, we felt unsupported by the school, but it wasn't until year 9 that he started refusing to go. We moved him to a different school for year 10. They couldn;t have been more undrestanding - making adjustments to his timetable, giving him access to a quiet room, giving him a pass to leave lessons etc etc, but by that point, I think it was just too late.
He has anxiety and panic attacks. He has never been formally diagnosed because I can't get him anywhere near CAHMS - around here, you have to be actively psychotic or suicidal to see CAHMS and several referrals have all been refused saying "He doesn't meet the criteria". Our GP referred him for counselling, but wouldn't prescribe any medication without CAHMS seeing him. Total stalemate. He is also autistic - this was diagnosed privately because the waiting list is about three years long for assessment here currently and he wasn't referred until he started at the new school because the old school laughed at me when I expressed concern he may have ASD.
I paid for a private psychologist out of desperation, which has helped, but he still cannot put himself in certain situations. I have tried everything to try and get him to go to school - being tough and removing tech, being kind, cajoling etc etc. You name it, we have tried it. It doesn't work. I never know which is the right approach to take and I am worried I have damaged his mental health and made him worse by trying to make him go when he isn't happy to go. I have been sat outside school with him on the car, wanting to go in, but having a full on panic attack at the thought of it. If he won't go, he won't go and there's nothing I can do that will make him. Currently, home is his safe place and he trusts me and his Dad - if we push too hard, he won't trust us any longer and home won't be safe for him any longer and then what would happen?
He isn't as bad as some. I would say his attendance has been around 70% for year 10 and 11 and he managed to do really well in his GCSEs. He went back for sixth form and came home after an hour, saying he couldn't go back. He's not in a small independent school and managing reasonably well so far, although his attendance isn't perfect.
We are lucky that we can afford to pay for help and I really feel for people who can't. It has been the most stressful few years of our lives, it is truly awful to go through, so please, everyone saying we should just make them go - it isn't that simple. We should get them diagnosed and medicated - Ha Ha, I'd like to see you try. Get them properly assessed for neurodiversity? Alchemy is easier. Just make a panicking teenager go to school? Well, if you have at least two strong men who can drag him there kicking and screaming and don't care about his mental health getting even worse? And even if you get him there, how do you make him stay?