Technically speaking a prospective employer can ask a past employer if you worked there and whether or not they'd hire you back. They aren't supposed to ask exactly how and why you left the company. Chances are that if they asked Disney if they'd hire you back, they'll say 'no'.
If it were 'a few years ago' would it do any good to contact Disney and see if you can get your status changed? If you've had a good work record since then and can get a couple of references showing you as trustworthy and conscientious, maybe they'd lift the restriction.
If not, was your work for Disney short enough that you can leave it off your resume without creating too big of a gap?
I don't get why your family giving you money would lead to termination, but I don't know Disney's rules. Is it something that could be explained without too much of an appearance of gross dishonesty or duplicity? Like "I let a relative use my employee discount"? That would be different than "My brother paid me $50.00 and I let him through the turnstiles" or something.