I can see why this could be a problem for the agents because you are asking for an almost impracticable combination. Relaxed and child friendly don't normally coincide, nor does informal and child friendly. The best area for sun at that time of the year and to avoid heavy rains would be the Caribbean. Although it is a long haul flight the children should be ok on it, flights to the Far East are more difficult for them. You say that money is not a major criterion so a good class ship from cruise lines like Celebrity or Princess where children's facilities are provided together with a certain amount of decorum. Although Princess is a little more noisy than Celebrity and the food is better on Celebrity, Princess has a more British attitude. I would also stay away from cruise itineraries which include La Guaira, Jamaica and Tobago as these could provide a certain amount of danger. I hope this is helpful. Lucy X.
Caribbean is best for weather. I agree that Princess are a good cruise line to holiday with if you're looking for relaxation and something for the children. If money is no problem, some of the newer Princess ships have the 'Sanctuary'. You pay $10 for a morning/afternoon, but as no children are allowed it is pure bliss! Other Princess ships already in service are having this feature fitted in the coming 24 months as it's proved highly popular. However if you don't want to spend the money the ships do have 'adults only' pools with bathing areas - very popular.
For children, the larger Princess ships are best (Crown, Ruby, Emerald, Caribbean, Grand). They have more facilities as they are larger and can provide far more. They have video games, chill-out areas, clubs, plenty of pools, MUTS (Movies under the stars) screen (they often played 'guiutar heroes' during early evenings on MUTS before the big movie). You can also leave them in the company of the clubs if you fancy an 'adults-only' excursion! I also agree with Lucy that some destinations are best avoided - stay on ship. A lot of people have avoided Caracas - unless on a ship excursion.
Visit www.Princess.com for more details. But I reccommend booking with a cruise specialist (on the internet or by phone). This site, cruisefinders or cruisedeals are good sites to visit. Whichever cruise line you choose, (Princess, Royal Caribbean, P&O, Carnival, NCL) you'll have a great time! BUT ALWAYS BOOK WITH A CRUISE SPECIALIST - NOT WITH A HIGH STREET TRAVEL AGENT!
Can I assume that these were High St travel agents? The reason you came away with differing results is no surprise, Jack of all Trades, Master of None. Speak to a Cruise Specialist, such as this sites Freephone number & speak to people that actually go on cruises & not just dream about them. Give them all your requirements & expectations, get sound advice, get quotes from other cruise agents, all of which should beat the High St prices. If the kids are high on your list of concerns, Royal Caribbean beat everyone hands down. Good Luck ......Wilba.
Most cruise ships will have plenty of things for a nine year old to keep them occupied but your nineteen year old may find some ships have little to offer in the way of entertainment (read that as "boring"). If he/she is happy to sit in the sun/read and stay with you in the evenings then it may not be too much of an issue but, as suggested by Wilba, I think a large modern Royal Caribbean ship would be a good option for both your children. It may not be as informal as you want (and probably full of Americans), so dressing up in the evening would be the norm. For true informality Ocean Village would be an option with no dressing up and 24 hours buffet food. Unfortunately I personally don't think OV offers much for a 19 year old (although your nine year old would be fine). I know I have concentrated on your childrens requirements but, if they are happy then you will be happy. Hope this helps. Have a good cruise.