You do need a handicapped parking permit to park in the handicapped parking area.
The state issued hangtags are valid the same way as a handicapped license plate is. If she has either a wheelchair or an
ECV that you are bringing with you, your only option is to park in the handicapped parking areas. When we were at WDW last week, we parked at the handicapped lots at both Epcot and MGM. Each time we went, the lots were quite full and we were lucky to find a spot and most of the time had to walk the full width of the parking area to get to the entrance (DD had a wheelchair, so we had to park in that area). As wee drove into each park, the CMs told us the handicapped parking was pretty full and if we could not find a spot, they would have to find us something else to do (like have DH drop DD and I off).
Another option with a wheelchair or ECV (if you are staying at one of the WDW resorts) is to use the bus transportation. Buses, monorails and most of the boats are wheelchair/ECV accessible and drop you off very close to the entrance. For MK, unless you are staying on one of the monorail resorts, it is best to take the bus. It drops you off very close to the entrance. If you park, you have to ride a tram to the Ticket and Transportation Center and take a boat or monorail from there.
If she doesn't have a wheelchair or ECV, there are some other options.
Here is what Disney has to say about Handicapped Parking in their Guidebook for Guests with Disabilities:
Theme Park Parking (Standard parking rates apply)
Guests with the ability to walk short distances and step up onto the courtesy trams should park in the main parking lots of Magic Kingdom® Park, Epcot®, Disney-MGM Studios, or Disney's Animal Kingdom® Theme Park. The courtesy tram will transport Guests to the Entrance Complex. Parking for Guests with mobility disabilities or who are traveling with personal wheelchairs is available adjacent to the Entrance Complex at each of the four Parks.
Guests should inquire at the Auto Plaza for directions on parking options.
The courtesy trams that are mentioned
only go to/from the regular parking lot; they do not service the handicapped parking areas.
If she is planning to rent a wheelchair or ECV in the parks, there are some courtesy wheelchairs available in the handicapped parking area that can be taken from the parking area to the wheelchair/
ECV rental area. They are first come, first serve with no guarantee that they will have any available. We were just at WDW last week and often saw the 'corral' for the wheelchairs was empty (so none were available). So, if she is planning on renting in the parks and can step up unto the trams, it's better to do that.
If she is able to ride on the trams, tell the parking lot CMs when they are directing you to a parking spot. They DO save some spots close to the parking tram stops for people who have difficulty walking.
There is no tram service to the Handicapped Parking area and if it is busy, you can end up parked quite a walk away.