We sail in September on oasis of the seas. We are taking our 4 year old and almost 2.5 year old.
1. Can our 2.5 year old go do the dinner time and after dinner activities so we can go out? Or no because he’s not 3 yet?? He’s mature for his age, fully potty trained, talks great, etc...
2. Can both parents go do an excursion on an island and leave the kids on the boat? Or how do you feel about young kids doing an excursion in Mexico due to the potential bad areas?
So the answer to your question is yes and no. At 2.5 your son will not be old enough to participate in Adventure Ocean like your 4 year old will be able to. That being said, He can go to the Nursery onboard. There is an hourly fee, usually $6 per hour before 5pm and $8 per hour after 5 pm. If you drop him off early enough they will order some food for the kids that are there to eat for dinner.
Your 4 year old can stay in kids club for their dinner if you would like as well, but you do have to sign them up for that one and it is not always offered every night, so its best to double check the schedule when you get on board.
Another option would be to schedule your dinner for after 7pm when the Nursery and Adventure Ocean would both be open as part of their regular hours. (They do open later on the first evening so I wouldn't schedule an fancy dinners that night.)
You are welcome to leave both your children on board while you get off the ship to go on an excursion. We have done this many times with our kids as occasionally we want to do something that we know they will not enjoy. When we choose to leave them on board, we make sure we are back with plenty of time before we sail away just for piece of mind.
If you wanted to take your kids with you, I would say you are pretty safe, especially if you stay on Cozumel. Personally we have not ventured over to mainland Mexico for any excursions as the ferry that takes you there is often referred to as the "Vomit Comet." For some people they have no problem on it, but if the seas are choppy, it can be a rough ride across the channel. There are plenty of awesome things to do in Cozumel, so it just depends what you want to do and if you think your kids will enjoy it.
When we opt to go to the beach in Cozumel we usually bring our kids with us, but if we just want to walk around downtown and do some shopping and eating, we tend to leave them on the ship!