I would think that a taxi would cost aprox $40-$45, I taken a taxi twice in WDW once it was a van and a second time it was a regular car. If you ask the valet service to call a cab and you think you would need a van I am sure they would request one. I would think though that a car should be large enough.
You can use a town car service, the cost from WDW to Universal one way is aprox $30.00. When you make arrangements just let them know you are going to a resort and not the park.