NCL, Carnival or RCCL would all be good choices, my kids are 5 and 8 and will be going on their 10th cruise in November, they have been on all three lines and loved every one of them and these three lines certainly meet the needs of parents with kids. NCL will probably have the most flexible dining arrangements, but there is another strategy we have used with success. Generally speaking the kid's club opens for the evening at around 7:00, so if you have set dining times, you could choose late seating and take the kids to the buffet around 6:30 p.m. to enjoy a nice dinner of stuff kids love then allow them to attend the kid's club while the grown-ups enjoy a nice quiet romantic dinner an hour or two later. Some four year olds have difficulty sitting through long meals...especially when the only thing they have on their mind is going to play at the kids club lol.
If your little one is still napping, I would probable spring for a balcony or minisuite to give the grown ups a place to hang out while the little ones are asleep. On the NCL Pearl we booked a mini-suite and I recall a privacy curtain that divided the bed from the sitting area.
The other thing you could look into is a Family suite on RCCL's ships that would accomodate all 6 of you and provide 2 separate bedrooms and 2 bathrooms. RCCL also offers in cabin sitting which I have used and was very pleased with our experience. Hope that helps.