There are some very good alternatives. If you weren't cruising with kids, I'd highly suggest Virgin Voyages, but with kids, there are still good options.
We haven't cruised Celebrity, so I think that the previous poster summed that up, but I can suggest that you may want to look at a ship in Princess' Royal class of ships (Royal Princess, Regal Princess, Sky Princess, Majestic Princess, Enchanted Princess). Classy, but not too high-end is EXACTLY how I would describe Princess. Also, there are little touches that we appreciate..
- Wifi. The new Princess ships are what they call "Medallion Class", so you get a little puck for your lanyard that essentially acts as a magic band for your whole trip. You don't even have to scan to open your door. It's pretty cool. These ships were built from the ground up for Wifi coverage. My wife has worked some from the nice open deck behind the Horizon Court and she said that the wifi was excellent. Never had an issue with it. Even streamed a football game with no problem.
- You mention allergies. My DW has a gluten allergy and not only is the head waiter in the MDR usually on top of it, the chefs in the buffet will come out to discuss. On Regal Princess, they would make my wife "off-menu" items just by her asking. On a side note, out of the many cruises that we've done, Regal Princess has by far the best buffet that we've had. Also, I believe that room service is still complimentary.
- Like
DCL, there is a poolside grill option. This was one of the many things we found that we missed on
RCCL (also, why does the Oasis shut it's ice cream down at 5:30?????)
- Princess ships with an Alfredo's (an included, casual sit-down restaurant) are a plus. When you see all the posts about Princess having the best pizza at sea, this is what they are talking about. There is also pizza out on the Lido deck, but while good, it's not as good as Alfredo's. (Their calzones are really good too...). The burgers on deck are good too, but I have to give credit where credit is due, I think that Guy's Burgers on Carnival takes that award...
- Princess does have a very underrated kid's program IMHO. They partner with Discovery channel, so there is a lot of Shark Week/Mythbusters type stuff. We saw on our last Princess cruise where they took the kids in the galley as a "Jr. Chef" program and let them cook in there. Not sure if that's going on now because of COVID, but all the kids seemed to love it. My DD is now 18, and she actually prefers Princess for teens (don't get me wrong, she loves DCL too...). That being said, she's not a "waterslide/rock wall" kind of person. If you are looking for that, then RCCL, Carnival, or NCL would be what you would want.
- We really like Princess' entertainment too. Not so much the main shows, though some are not bad, but they have a number of spaces where they always have something going on, be it game shows (Yes/No is our favorite), trivia, comedy (usually an early 'Family' and later "Adult" version, educational talks (mainly in Alaska), etc. They also have a LOT of live music, either in the Piazza or in the lounges. Our all-time favorite was when we stumbled into an "Irish Song sing-along" with an Irish band on Emerald Princess. Let's just say I'd want my kids to at least be teens for that one, but man was it fun... Another cool thing (I thought) on our last Princess Cruise on Regal Princess was apparently, the crew had formed an all-crew rock band, so Princess let them play one night. It got the whole ship into it.
- Like DCL (and Virgin), Princess does not charge for in-room movies. They were $11.99 on Oasis. (Not sure if they are included on Celebrity.)
- Every sea day, in the Crown Grill (steakhouse)/Wheelhouse Bar area, Princess does a complimentary British Pub lunch. I love their fish and chips, DW likes the shrimp. It's a nice change.
- Oh, and you don't have to check-out towels like you do on RCCL...
I might even throw Holland America in here as well, but I think that the age demographic would skew even higher on HAL than it would on Princess/Celebrity, but that would depend on the itinerary and the time you go. Any of these lines will have plenty of kids during times when schools are out of session.