Hi James!
Having two young ones myself, I've found it easier to visit during the Fall or Winter seasons, generally non-peak periods for the Disney parks (excluding holidays such as Thanksgiving and Christmas). There's less traffic, smaller lines, and the weather in Florida is much milder than other areas of the US during these seasons.
In terms of deals, Disney generally offers promotions throughout the year. You can check here periodically for any special offers.
You can also sign up with your email address here and receive news, updates, and promotions on Parks and resorts.
Finally, if you're a member of AAA or similar groups, you can capture promotions offered thru their membership sites as well.
Good luck on your planning and preparation!