I think about a half day for DCA is a decent plan with that age group. I can see the appeal for entering after 1 since your hotel is right there, but it may actually be better to start the day at DCA (don't forget to switch your park reservation over to DCA for that day if you do this). You can do all the rides that interest your family and probably do it fairly easily with short waits-you might not even need LL at all if you do it right-and then the hotel is right there in the same park when you run out of steam.
The only show that would need a reservation (Disney calls it a Virtual Queue) is World of Color, which becomes available at 12 PM. Each member of your party needs to have entered DCA in order to make the reservation, which would be another reason to start your day at DCA, since otherwise you can't join the queue until 1.
Lightning Lane is same day only. Make sure you've linked all of your family's tickets together on your Disney account before you go. Each person can get Lightning Lanes once they have entered a park. Look at the tip board page on the app and it will tell you what time is available; if you like the time you see, book away! You can then get another Lightning Lane once you've used the LL OR after 2 hours, whichever comes first. Note that some Lightning Lanes are NOT included in the general LL groupings and have to be purchased individually (Rise of the Resistance, Radiator Springs Racers, Spider-Man webslingers). My one caveat with LL is that a lot of the options are for the more thrilling rides-while there are things on there that all ages will like, it's probably something worth thinking about. As said, the crowds don't usually show up til around 11, so if the park opens at 8 (and you're ready and in the park at that point) you may be able to get on some things without waiting too long, so you might not necessarily want to start booking LLs immediately.
If your ticket is a parkhopper, it will be flagged in the system and you won't need to do anything extra. The only difference from a one day ticket is that after 1 PM you can go from one park to the other. You can do this as many times as you want, and it's easy as the parks' main entrances face each other. You don't need to go through security again or do anything special, just move from one entrance gate to the other. If there isn't a line at the turnstiles you can do it in less than five minutes. Note that parkhopper can only be purchased for length of stay-so if you're there for three days, you can hop on all three (so you can't just pay less money to hop on only one day of your trip).
If you don't get parkhoppers, you can still re-enter the park you chose to visit that day by presenting your ticket at the turnstiles. If you don't get parkhoppers I would do DCA as the middle day of your trip so that it can become the down day between two more active Disneyland days.