What you are asking about is a Guest Assistance Card.
There is very complete information in post 6 of the disABILITIES FAQs thread. You can find that thread near the top of this board or follow the link in my signature.
You request a Guest Assistance Card (GAC) at the first park you go at Guest Relations. You go there with your children and explain their needs. You don't need a letter.
The GAC will be good at all the Theme Parks for the length of our stay.
GACs are not passes and are not meant to shorten waits. They are meant to be a way to let Cast Members (CM) know some basic information about your special needs so you don't have to explain everything to each CM.
So, your wait may be the same time, but in more suitable conditions.
Depending on the attraction, how busy the park is and how many other people with special needs who are waiting, using a GAC can even take longer than just going into the regular line. GACs are not handled the same at each attraction because some attractions ont hve ll the possible accommodations that others have. And, even at the same attraction, on the same day, the same person with a GAC may be handled differently because of things like staffing level, number of people already waiting and/or a quieter waiting area being temporarily not available.
Because their kids handle the different treatment, some posters prefer to use the Fastpass system for attractions with Fastpass because it pretty much works the same each time. They use the GAC for other attractions.
A lot of people find that using a touring plan and fastpasses is very helpful.
GACs are only helpful in attractions, but touring plans can help you to be in the least busy part of the least busy park. This can make your waits much shorter for attractions, to the point that some people find they hardly use the GAC.
Touring plans also help in places a GAC can't, like restaurants, bathrooms and just walking around.
You can find a lot more info in post 6 of the FAQs thread.
