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Your first step will be to find a cruise line who will take such young babies...most will not take babies under 6 months of age ...some will not take babies under 12 months of age.
Morris has given you the answer.......Two babies........Two words to consider......Noro Virus!!!......Wilba.
Another two words to consider.... don't do it (OK that's three, but you get the idea). You really don't want to put such young babies in a creche with hoards of other kids with lord knows how many germs passing round. I certainly wouldn't risk the Caribbean even disregarding the long flights. There are several reviews on this site outlining the long waits on aircraft, coaches and embarkation points to board the ships. Plus your childrens' vaccination programme is not complete. If you have your hearts set on a cruise, Norway would be safer for your children's health, but Norovirus is still a risk on any ship. Have you considered asking a kind grand parent/aunt to have the kids for a week while you try a short cruise to see if you would like to take the children next time?
Young babies travel better than older kids, we took both ours on long haul flight at 7 months and as long as you follow a sensible hygiene regime they will be fine. We were greeted with countless oohs and aahs with well meaning travellers telling us how brave we were! you'll be fine its when they get to 2 they start causing problems, now ours are 4 and 5 all is well again, and norovirus also exists in the UK! Sorry we didnt cruise with ours at such a young age so cant offer any suggestions as far as ships go but take it from a family who are well travelled with babies, to places such as the caribbean and the far east they are a pleasure to take at that age, and I was fully supported by my G.P. and Health Visitor in this.
If you can hang on until your twins will be 12 months old, I could highly recommend Cunards Queen Mary or Queen Victoria, who cater for children as young as 1 year old. Their facilities for both babies and children are amazing and they have fully qualified English nannies, giving you young parents some much needed time to yourselves to relax, wine and dine etc., at the same time as just being a few steps away from your children (and with a bleep) to be contacted if necessary. I speak both as a Grandparent and parent, and we have used Cunards facilities for our two very young grandchildren. Cunard ships never seem to be overun with children and therefore they get very good close and attentive care. You could try sailing from Southampton (so you could take as much luggage as you need with the least possible hassle) either on one of the Fjord/Mediterranean/or a 4 day northern europe cruise which you could use as a "taster". Speaking from personal experience with my extended family - I say go for it and enjoy! The only downside I can think of is your young twins who will have to be 12 months old, will probably get spoiled to bits!