I'm glad you asked! I used to travel frequently for work, and after a couple of mishaps with my checked luggage, I committed to traveling carryon-only, and I've never looked back. Here's how we do it (to summarize, we bring only what we need, with a carefully-curated packing list that we stick to):
1 - Each member of the family has a rolling 21" carryon suitcase for his/her clothes and shoes. (The bags are the traditional style with two wheels, which have far more interior space than 4-wheeled rolling bags). For a trip to Disney World, those suitcases will hold (rolled carefully to reduce wrinkles, and placed into packing cubes) 5 or 6 warm-weather outfits (if our trip is going to be longer than 5-6 days, I simply bring half the clothes we need and schedule a relaxing morning doing laundry by a quiet pool, mid-trip), a swimsuit, PJs, underthings, and a pair of hiking sandals. An eBags pack-it-flat toiletry case with the whole family's toothbramazementekeup and hair things, etc. also goes into the top of my bag. Because the kids' clothes are smaller, their carryons are only about 75% filled after their clothes are packed, so breakfast foodstuffs and miscellaneous items (a laundry bag, rain ponchos, glow sticks) get added to their bags. DH and I each slip our 3-1-1 bags (mine has cosmetics and toiletries, his is chock-full of sunscreen) into an outside pocket of our carryon, for easy access during security screening. Fully loaded, each carryon bag weighs about 20 pounds, so our kids (every since their first Disney trip at ages 4 and 6) have easily been able to pull their own bags.
2 - DH and I also each have a "personal item" for the plane -- a backpack for him and a tote bag for me, one with the strap on the back that allows me to slide it over the handle of my carryon when heading through the airport. My bag contains my park bag (a tiny crossbody purse with my ID, cash, travel documents, phone, 3x5 itinerary cards with confirmation #s, our MagicBands, etc.), a mini First-Aid kit with Band-aids and Tylenol, wet wipes, sunglasses for me and my daughter, my camera and any other electronics, earbuds and chargers (packed into a clear pouch for easy inspection during security screening), and any in-flight snacks for the family. DH's backpack contains his ID/cash, sunglasses for him and my son, his own electronics and accessories, and any extra items the kids may want in-flight. For our first trip, we also had the kids bring backpacks as their personal items, but we found that they just got in the way, and the children only had a book or two, and a pair of earbuds that they wanted during the flight, so we just consolidated them into our own personal items on future trips.
3 - We wear our bulkiest clothing on the plane: long pants, sneakers, a short-sleeved top, a hoodie, and for my husband and the kids, a ballcap. This saves space in the luggage, and is generally appropriate for the weather at home anyway. We usually travel to WDW in fall or spring, and most times we never had to break out the hoodies or jeans again until the flight home, but they're nice to have in case there's a cold snap. If we think we'll want to change into shorts in-flight or as soon as we get to Orlando, we keep an extra pair of shorts in my husband's backpack.
Easy-peasy!