Have you told your ex that to get her on Thursdays?
That is his court ordered time. If you have to hire a babysitter (obviously one who can handle caring for a child with a severe handicap) while you get out, you can ask that he pays for it. If he doesn't want to exercise his time, that is his choice. But he's going to have to compensate you for any extra expense you incur as a result of his not exercising his parenting time.
Does he take his week-ends with her? If so, use that time to do something for yourself that you enjoy doing.