Hi SandraC - took a look at your list and here are my comments/concerns . . .
Cuba and the Dominican Republic - I have only been to Cuba myself (and that was over 10 years ago) - my concern with both of these destinations is health care - God forbid anything would happen but I think you would have a better chance of getting help in Jamaica or Mexico - as far as the properties in Cuba go - if they are in Varadero you have to be careful about where they are located as I have heard that there is an area of the beach there that is very close to an area that smells terrible - I don't know if this is an all year thing but I have heard that there is one end of the beach that is not a good place to be - could be rumour but you never know
Domincan Republic - I have not heard of the Royal Uvero Alto in Punta Cana and it is not in my Official Hotel Guide - the website states it is an "adults only" all-inclusive though so if you want to go with your children, this will not be an option - some all-inclusives are adults only (usually 16 years old and up) so you have to watch for this before you book if you have children
Jamaica - Beaches - this property is located in Ocho Rios so it will be a one hour to one and a half hour transfer time from the airport in Montego Bay - it is also an adult's only property for 16 years and over - it looks beautiful and has a Superior First Class rating in the Official Hotel Guide - Beaches is a part of the Sandals chain of properties and Sandals has a great reputation in terms of service and food so this would be a good choice
Cozumel, Mexico - Paradisus Mexico - out of all the properties you listed, this looks to be the most kid friendly; although I did see something mentioning 3 guests only per room (I can't remember if this was for this property or for the Tulum Village - check the websites again) so you may need to check this out if you have 2 adults/2 kids - they have a Children's Club for ages 2-12 years old and most resorts will only look after your children if they are at least 4 years old and toilet trained - I don't know if I would leave my children with some of the attendants they have there and if the ratio of kids is high (ie. 10 kids at club to one attendant), I would be wary. In saying this, however, I did leave my 3 and a half year old with her 6 year old sister at the kids club at Viva Vallarta last year as she begged me to leave and let her do the crafts/play with the other kids (I checked back with them often though)! There were also only 4 kids with 2 attendants so I thought the ratio was pretty safe! In my Official Hotel Guide it lists the Paradisus Cozumel as a First Class property built in 1972 and renovated in 1997. The only other concern about this property is its location - would you be flying into Cozumel - if so no problem as it would probably only be a 10 to 15 minute transfer from the airport - if you have to fly into Cancun and then transfer to Cozumel it will require a 1 hour transfer by bus/car and then a ferry ride to Cozumel which can be rough (when I did the ferry transfer from the mainland to Cozumel, quite a few people were sick but I think that it was an exceptionally rough day on the seas)
Tulum Village, Mexico - this is a one to one and a half hour drive from Cancun's airport - this property looks like the quietest out of all of them - no mention of kids facilities on the website so you may want to check that out - it is not listed in my Official Hotel Guide so I can't give you arating (if the properties are not listed in there, it may be because they are not affiliated with a major hotel chain or they did not pay the fee to be part of the listing)
I hope this helps you out - let me know if you need any more info on other properties you can consider.