MomV. Having been on all of the lines you mentioned, Im sure you and hubby would enjoy any of the lines. I see you have cruised Celebrity before so you know how nice the Solstice class ship is.
I have done Celebrity in the Greek islands, Europe and Mexico. Celebrity is great for adults but not know for the night life for the 20's, I took a 30 y/o with me on Celebrity who said not enough night life. Now if your kids don't want to party and want to relax in style, go to lectures and have great food, then Celebrity it is. Celebrity is my favorite line.
I did HAL to Mexico and it was very much the "Senior Set", great food, but nothing to spicy or out of the norm, the ships are set for seniors, not a party boat. I think the kids will not be happy with it. I joked that it was a walker and wheel chair convention, I felt young on the ship and I was 40.
The new NCL ship has tons of things to do for the kids and lots of night life. I would check if this NCL ship has the bathroom that has a sink in the cabin with separate water closet and separate shower closet, if so may not be the privacy you want if all are sharing the same cabin (shower is a closet so you step out into the cabin) Also if doing NCL I would suggest the (dining package) extra fee restaurants as the MDR food is not to great on NCL. The French restaurant and steak house were great on NCL. If they do a sea day Indian lunch for $ 10.00 each it was great.
Carnival, well it is the fun ship. Lots to do for evening entertainment, great comedy club, shows, sports bar, piano bar and lots musicians around the ship, Water slides and mini golf. The food on Carnival is good, the steak house is fantastic ($35.00 each but worth it) the 24 hour Deli and Pizza are good. If it has the Blue Iguana Cantina awesome taco's and burrito's
If I was picking with the kids in mind I'd go for Carnival. It has activities the kids would enjoy, good food, good entertainment and will attract passengers around the kids age. I have always had fun on Carnival, but I know when I book it, lots of noisy kids (the Serenity deck is great, 21 and older only) Lots of young people partying and a mix of 40's to 70's. Carnival is the floating Walmart but it is lots of fun.
If your leaving from a home port check with the Cruise line how much soda you can carry on with 2 kids carrying on soda could save you a small fortune. Have a great cruise and please post a review.