So...multiple threads on MN which suggest it's perfectly OK to leave kids alone whilst going to the shops, suggesting we mollycoddle them, kids are much more independent than we think, never did me any harm blah blah.
Might I humbly suggest the furore here is because OP has mentioned Business Class and dontchaknow we never had a holiday till I was 43 and even then we got the bus to Margate...
Because the truth is a) 10 and 13 year olds are perfectly competent b) being in an enclosed plane cabin is a lot safer environment than home alone with matches and burglars and the drinks cabinet c) am sure the OP will be popping back frequently.
Tbh I think the treat of being alone and treated as adults will matter more to them than access to free bubbly in business. And two business tickets mean you can all go in the lounge either end, which will be great.
As for 'family time' - has anyone ever actually enjoyed family time with a 13 year old on a plane? Or any child, come to that? Am sure if they're anything like mine they will pop on the headphones and start playing with the entertainment system before take off (which is great!) The quality time is on the holiday itself.