I find for popular places that you get the best deals about 6 months out. I then check back periodically and then if for some reason there has been a price drop I just cancel and rebook. Usually the cancellation policies are pretty lenient that far out.
For tropical places, you usually get the best deals mid September through October, the first two weeks in December and mid-April through the end of May. Has to do with most people’s school and vacation schedules with the holidays. It looks like you are taking kids so that may not work for you, but for instance, we got a place in Costa Rica last December for about a third of the price you would pay in February just because those two weeks are slow for them.

We usually go to the pacific- Hawaii etc in the fall and Caribbean in the spring to avoid hurricane season in the Caribbean but if you don’t mind the risk, prices are cheaper there in the summer through November. I would pay for trip insurance though.
Aruba, Bonaire and Curaçao are outside the hurricane belt and most of the resorts in Costa Rica are on the pacific side so they seldom get hurricanes the rest of the Caribbean gets but that is the rainy season there too.

For non tropical places, ski resorts, mountain resorts etc. High season is usually based on what kind of activities they cater to so the cheaper times will vary but places like Banff that are year round locations are usually cheaper after the best weather in the summer in the Fall and just after the snow melt in the Spring. Still beautiful but not optimal for all activities.