Thanks for the shout-out,
@Tuvalu! I live for this kind of topic.
Here are my general suggestions, OP:
1 - You're right that packing for 14 days would be a pain! Do pack for one week instead of two, and plan to do laundry half-way through the trip. Just pencil it in for a day when you're in the mood to spend a couple of morning or afternoon hours lounging by pool, and you'll find it doesn't feel like too much of a chore. (If you're staying onsite, the laundry rooms tend to be near the pools, and you can conveniently monitor the progress of your laundry through an app.). Doing this will cut the number and size of the bags you have to lug around in half - not to mention the amount of laundry you'll have to do when you get back home.
2 - When I say "pack for one week," I'm assuming for each person: 7 warm-weather outfits, plus 2-3 extra shirts for sweatier days; underthings and socks; swimwear/rashguard; nightwear; 2 pairs of hiking sandals or flip-flops. Anything bulky or heavy - sweatshirt, jeans, sneakers, hats - should be worn on the plane. If you want to bring more clothing than that -- e.g., 2 outfits per day so people can change when it's hot -- you may have to consider packing for 5 days instead, and doing laundry twice, or bringing those bigger bags and checking them. *Tip: If your family, like mine, tends to own a lot of athleisure-style clothing in super-light, moisture-wicking, Under Armour-style tech fabrics, you'll find that all bets are off, and you may be able to fit at least double the number of outfits that you'd normally expect to be able to bring...
3 - For each person, 1 weeks' worth of clothing should fit into a standard 21" rolling carryon with room to spare - you shouldn't even need to check any bags unless you want to. I like to use packing cubes, color-coded for each family member (not compression bags: they'll wrinkle everything up, add tons of weight, and facilitate overpacking). There will be a little bit of space left in each person's bag (and quite a bit in your younger child's bag, as their clothes will be smaller!), which can be used for toiletries (don't forget to put liquids and gels in 3-1-1 bags if they're going in carryons), meds, and miscellaneous items like disposable rain ponchos, cooling towels, etc. (and of course a large fabric or mesh laundry bag, powdered detergent pods, dryer sheets, a bag of spring-loaded clothespins etc.), and breakfast items or snacks for the hotel room.
4 - Make the most of your "personal items" for the plane. You can each bring a tote, backpack or small duffel (or whatever you are planning to use for a park bag) with: wallets/purse, sunglasses, phones and chargers/power packs, earbuds, gum/chapstick, water bottle (fill it up after you're past airport security), comfort items for the kids, wet wipes, face masks (if needed), etc.
5 - Make out a packing list ahead of time, check it twice, and resist the urge to throw in extra things at the last minute.
6 - Unless you have a special need (e.g., I can't travel without my dandruff shampoo), don't pack anything that the hotel provides (towels, soap, pillows, shampoo/conditioner/body wash, coffee filter packs, etc.).
7 - If you're worried things won't fit, take a few minutes, a few days before you leave, and "practice-pack" your suitcase with the outfits you've selected. Since you already have packing cubes, I suggest using them -- either roll your clothes and place them in the cubes, or fold them using a folding board that is sized to match the packing cubes. (I made one with duct tape and an old cardboard box, which folds everything to the same dimensions as my packing cubes. It cuts my packing time in half or better, minimizes wrinkles, and has lasted for years!)
Instructable here, if anyone is interested:
Luggage recommendations: I tend to buy luggage that is decent quality but on the inexpensive side, so on the off chance something happens to it, I haven't lost a big investment. My current favorite bags -- both purchased at different times from ebay at a huge discount off of retail, because they were both unopened store returns -- are a 21" Delsey Helium Sky rolling fabric bag (it's a 2-wheel rollaboard: advantages are that you get extra space with 2 wheels instead of 4, the fabric has some "give" if you need to stuff it, and this particular make and model is really well-made and tough - I paid $80 for it), and when I feel like cruising with 4 wheels instead of 2 (with an attendant sacrifice of a couple of inches of space in the bag) or need to protect something fragile, a no-frills hard-sided 21" Coolife spinner, which cost me $50.
Of course, I am a little less concerned with my bags getting damaged than most people are, because we never check luggage. (I used to travel extensively for my job, and saw enough instances of lost/delayed/damaged luggage that I vowed to avoid it in the future). That way, my luggage stays with me, and I don't need to worry about it getting lost or handled roughly. Obviously your mileage may vary, and I realize that packing carryon-only isn't for everybody, but I can say that it's worked really well for my family of 4 in the 10 years we've been traveling together, starting when the kids were just 4 and 6, at a time when half their carryons were occupied by their "must-have" stuffed animals from home.
If you'd really rather pack those bigger bags and check them, no worries -- with 2 big bags and 2 carryons, you shouldn't have any trouble fitting at least a week's worth.