Just back from Lemnos Neilsen holiday. I'll be honest - I'm a total package holiday snob and was worried we'd hate it, but we were desperate for a break that came with childcare. Well, I'm a total convert and so is my partner.
So the beach isn't the most beautiful.... But, on the plus side - The hotel has just been revamped and is perfectly nice (great interconnecting rooms if you have more than one kid). Yes there are elements of the upmarket Butlins, but it is an 'Activity Holiday'. The key thing is ALL the staff are amazing, especially the childcare. Everything is done for you. There are sleep clubs free twice a week and you can book more. It's a great way to spend time with you partner doing something new and different (we learnt to sail dingys, again something I'd not really thought about before).
One question - how old are your kids? If you go out of school holidays, and at the end of the season, you'll find the number of nannies per child is very high. Our older toddler (just 3) has language delay and he was assigned a one on one nanny at no extra cost (in fact without asking). He went dingy sailing everyday too.
Don't be under any illusion you're off to see a remote and historic part of Greece. You'll see a tiny bit of the town and that's it. BUT, you'll have a really good break from the day to day grind, without a seconds worry about your kids as they'll be having a ball, and you may even gain a new activity style holiday.