Ships come in many sizes just like land based hotels and resorts. As mentioned, think of a ship as a floating resort. Norweign's ships other than the brand new Star are smaller. Try to book a ship that is about 5 years young and 80,000 GRT or large. Carnival cabins are larger and they along with RCI have a great kids program too. I agree with the suite, but if you can't afford it, get a Balcony with the fold down births. (fold completely into the wall or ceiling during the day) .The other child can sleep on the sofa bed. Worst case for space, book two adjoining outside cabins both @ 185 SF and you would have 2 bathrooms.
"I think I am afraid that the moment the ship leaves the dock I will be trapped and will not be able to get off. That is my first scenario." - It was mine Too. Choose an itinerary with lots of ports of call. You will know you are able to get off ship the next day.
2. What is the embarkation and disembarkation process...how long does it take are there long lines etc...- Depends on which port terminal building; Fll, Miami, San Juan, etc. (Heard NYC is a nightmare) Don't arrive at 1 p.m. when "everyone gets there". Sometimes there is no choice in this matter. The terminals are Huge with very high ceilings. Think clean renovated warehouses. Normal wait time in line about 1 hour or less. Princess has the best embarkation system going more like 15 minutes or less. Everything is done before hand and their desks are marked accordingly to deck and your cabin number. You will stand in line to join tour groups, to meet the Captain if you wish at the Welcome aboard party (optional), to get your formal picture taken (Optional - go after dinner instead), and to tender. Most ports you dock, so no tendering involved.
Disembarkation is by Color coded tags. Early flights & Special needs are first, then usually from the top deck down. People have to wait in public rooms, so crowds do form. This is a sad time too. The cruise is over. Customs is the other line. On my last Carnival cruise since 9/11, everyone including kids and disabled had to report at a designated time to a special room with their Government ID and clear customs. Thus lines getting off were shorter.
3. Do they have launches (tenders) go throughout the day to the islands you are visiting...you know like back and forth etc. - only on Tender ports; Grand Cayman, Belize, Playa del Carmen, Private Islands, etc.
All in all, the lines aren't that bad.