Oh God. I'm one of those irritating posters with the opposite experience.
We've been taking DD abroad for 2 weeks every year since she was 11 months old.
The first one was the worst - but only because we chose the wrong hotel. It was cramped, cold and too busy. Even then we still had a good time. Since then we've only gone 4* and with good reviews. We've had one holiday where it rained a lot, but the hotel had lots of indoor areas so there was still stuff to do.
I suppose it depends on the child. We go AI because luckily DD isn't a fussy eater - but even then, if she only ate chips and ice cream for 2 weeks I wouldn't worry. It's only 2 weeks.
We don't bother with bedtimes. When she was smaller she napped in the buggy if needed. We all had an afternoon nap. She went to bed with us when we did.
DH and I took turns to entertain her - pool, lilo, boat, bucket and spade, watering can. 2 hour 'shifts' whilst the other read/relaxed/whatever.
Kids clubs - 2 hours free time every day.
We also took a beach bag full of 'stuff' for her to do during boring moments (at night in a bar, quiet time in the room, the plane and travelling) - Easy craft kits from tesco. Paper, colouring books, pens. Play doh. That sort of thing. Later on I made sure my old phone was loaded with games that she could play. Now she has an iPad and a kindle.
We chose hotels with kids clubs, mini discos, playgrounds and party games. We took part in all of them! We looked for AI hotels that used to be SC - they tended to have better rooms or separate bedrooms.
When she got older we chose hotels with waterparks or Holiday Village type places. Lots of things for her to do so lots of relaxing for us. Last year DD was 10 and we worked in a couple of shopping days and 'history' days (easy to do in Greece!).
I'm more concerned about the teenage years TBH. I reckon that is going to be harder.