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We just did the 'independance of the seas' this is a fab ship for kids, they have a deck dedicated for them for example a fun pool/spash area.and some super equipement etc. look on web site.
This is only a observation as ew dont have any little ones but if i remember little ones were not allowed in pool if they had any kind of nappy on even the swim ones.best check out the line etc.
Also you need to check I cannot remember any clubs for the 7 month old and nearly 3 would have to be probably over 3 and no nappies. I think I remember that Royal caribbean has a club fgor 6 month olds but you have to stay - but at least it saves you taking lots of toys in your luggage.
Ocean Village may well be a good option with kids - it worked perfectly for us in July and was good value (we have a 2 year old son). Buffet dining with no fixed time made life very easy and meant there was always plenty of choice for children, but they also do a special children's tea too. The outside cabins are also spacious which is good when a few of you are sharing. The biggest plus for us was the Base Camp children's centre where we our son could either sign up to the sessions or we could go in there and play with him. There is also a family area outside the base camp with little tikes trikes etc. and a paddling pool that can be used by children that wear nappies. The base camp is also open on port days for you to use. In contrast we just did a mini break on NCL which did have waiter and self-service restaurants with a kids menu but it seemed harder to get a table when you wanted one. However, the thing that made us really favour OV over NCL was that the latter did not have a children's centre where you could play with your children without leaving them at an organised session, nor do they offer free provision on port days. They also didn't have anywhere that children in nappies could paddle or play with water. The OV2 children's centre also had baby toys there as well. Hope this helps.
Forgot to add that Ocean Village also have free a night nursery for under 5s (not sure if they take babies from 7 months though - I think it might be 12 months. Royal Caribbean do offer in-cabin babysitting service at a charge, but children can't got to their children's club sessions without parents unless they are at least 3 and fully toilet trained.
Best thing to do is collect all the brochures you are interested in and check out childrens facilities. Some lines don't cater for under 2 year olds .