Hello Amy and thanks for bringing such a great question to the Disney Parks Moms Panel.
I'm delighted to know you and your lovely family have planned a magical vacation to Walt Disney World Resort this coming April; I can just imagine how excited you all must be!
I absolutely understand the concerns for your families health as one of my own Mouseketeers has bronchial asthma and both my dear parents suffered with Chronic Obstructive Pulmonary Disease and I'm thankful to say we were able to enjoy many carefree trips to Walt Disney World Resort all together.
You may not realise but the old style Guest Assistance Card or GAC has been updated and is now known as the Disability Access Service Card or DAS.
Upon entering any of Disney's 4 Theme Parks I suggest seeking the advice and general guidance of a Guest Services Cast Member who will only be too happy to discuss the individual needs of your family members health issues, plus there's no need to worry about bringing along any medical letters or proof of disability.
For your further information you may find it useful to check out these great links -
Disability Access Service Card - Frequently Asked Questions &
Guests with Disabilities.
If I can help sprinkle any extra pixie dust onto your upcoming Walt Disney World Resort vacation please pop back to ask me another question.
Have a great Disney day.
~ Jane