Cruise but go Royal Carribbean. P&O definitely a bit like a floating holiday camp, Royal gives you lots more chances to avoid the joining in stuff and just enjoy the stuff on board at your own pace.
We paid £1k per person for a week in the fjords but this was a balcony room, so one of the best you can get without going into fancy suites etc.
You can book to dine just the two of you if you don’t want to do the communal sit with whoever turns up dining but I have always found everyone makes friendly conversation as everyone is in the same boat (no pun intended, honest...).
There will be two types of days; sea days where you are out on the ocean all day. No phon signal, definitely no wifi, spend the day enjoying the ship (ice rink, climbing wall, table tennis, pool table, gym, swimming pool, sports courts, reading on deck, either to do with the kids club or together as a family).
On port days definitely get off the ship. Will have phone signal and wifi here but also plenty to see and do so do research on each port and either book the organised excursions or go it alone. Tend to find that in major cities going it alone is cheaper, easier and you see more but some of the smaller ports, an excursion will help you get to see and do more.