I love the way your survey divides along gender lines! Different priorities!
I've done both (not at Disneyland but at Disney World). As a couple, staying off site and taking the hotel shuttle made tons of sense. With kids (and we went with teens/tweens and also a toddler, then later with the toddler at age 7), we found that "on the property) made the most sense. We could come back after lunch for nap time, and take turns staying with the little guy while the other adult took the older kids off to do something. Sometimes they need to chill out and be in the hotel pool vs. the lines in the park. Then you can go back around dinner time if people have energy. It helped to have a fridge in the hotel room - great for breakfast and snacks.
Friends rented a house with a patio/grill/pool about 2 miles away, and they found they were done with the park by 3, and just wanted to come home and hit the pool/relax/drink wine/cook burgers. They may not have gotten their money's worth on park passes, but it worked for them and the 3 kids.
We also used the Disney babysitting service, with total confidence and delight. We'd come back after lunch, put the little guy down for a nap, and one of us would do something with the 2 older kids. One our 2nd trip, we didn't have the older kids, just the little guy - still used the same sitter. It was fabulous. My husband and I had some adult time and went on rides or to attractions not appropriate for young kids. Sitters are bonded, pass criminal background checks, etc., and are used to dealing with kids in hotels who are far from home.
Take an umbrella stroller if you can - easier than a park rental stroller (which even big kids use) because you will have it on the hotel premises.