If all you want is powdery white beaches and warm seas outside of school holidays, I can think of a million and one better places than Mexico with 3 under 5! I work in the holiday industry, travelling to Mexico a few times a year with work, and have been to Mexico 3 times on holiday (once backpacking with sister and DH before kids, once with mother, once with kids) it’s fair to say it is one of my favourite holiday destinations ever! But I waited until my youngest was 7, and probably wouldn’t go now.
Why? You have to be so careful with the beaches. Since the sargassum seaweed started rolling in a few years ago, it hasn’t really stopped. It’s a problem in other parts of the world too, but Mexico has it particularly badly. The sea is often the colour of coffee, and if you don’t have a beach crew in your hotel on top of it, it can pile up and be a bit smelly. We didn’t go for the beaches - we went for the cenotes, the archaeological sites, the marine reserves, boat trips to see wildlife, zipwiring through the jungle seeing monkeys and giant blue butterflies and dipping in cenotes filled with terrapins, sleeping in hammocks in cabins by the sea and watching turtles hatching.
Cancun and Playa del Carmen are magnets for rich American kids getting away somewhere where they are the legal age to drink, and they drink ALL the tequila and beer, and you know about it! Especially in the spring. Don’t think that because you are in a naice hotel you won’t get them there. Security is an issue - even in very fancy resorts there have been drug gang shootings.
The hotels you would want to stay in are generally giant bland all inclusive chain resorts. If that’s your thing, you can find nicer and probably cheaper elsewhere. The main Cancun drag is a thin strip of hotels on a dual carriage way with shopping malls and nightclubs behind. Of all the places I go with work, this is the place I get the worst sleep due to the sheer noise of the place. Yes, even in a fancy hotel. Heading out to Playa del Carmen, the hotels become massive, and are set in their own bit of swamp. You need to be careful about mosquito bites, as it’s not just malaria but also chikunyunga and dengue are prevalent here. These resorts are very isolated from anywhere, and you won’t get much Mexican culture. They still have noisy drinking young Americans, sargassum, shootings, mosquitos, high temperatures (it will probably be about 30C and feel like a furnace on the beach at that time of year!) and food poisoning issues.
I love Mexico, it has been epic every time I’ve been, but the security is getting worse (I was robbed there twice in 2000, and have avoided it since but the general vibe is definitely worse.) Unless you are going for a site-seeing, activity holiday where you want to stay away from the main drag and get down with the local culture, I would not recommend it.
People have made lots of good suggestions. But if you want child-friendly powder white beaches outside of the school holidays, I would look elsewhere. Maldives, Mauritius, Thailand, parts of the Caribbean (you have to pick carefully here, as not everywhere is white beaches - eg St Lucia is amazing but volcanic island, any beach there is either grey rocks or has been imported. Sugar Beach has imported lovely white sand, the sand in Rodney Bay a bit more like orange builders sand! Dominican Republic, while devoid of much culture on the coast, is much more sandy with loads of AIs in nicer settings.) You will get stunning beaches in Greece, Turkey, the canaries, Middle East, lots of places closer or less time zone difference.
I’m not going to comment on the flight. I work on planes and would happily take my DCs all over the world on LH flights when they were young. Some families swan serenely around the world on long flights, I’ve seen families with one child having massive travel fails. Up to you if you think 12 hours on a plane with 3 toddlers overnight is your idea of fun.