That is a good question, I would probably say you can use them to go to both park since they offer that deal, so if they sell a 2 park ticket and rent strollers and things they must have assumed someone would use it to go to both parks.
I spoke with Universal. No you are not allowed to leave the park with the stroller, wheelchair or ECV. What you do is keep your receipt walk over to the other park and show them your receipt and they will give you one. I did ask about the ECV's and since they are limited quantity have the one park call the other one and see if they have one and save it for you.
An alternative for an ecv would be to rent from one of the outside rental companies. That way, you would have one available for park hopping without worrying about whether they run out.
These are the compnies that DIS posters report renting from most:
Care Medical: http://www.caremedicalequipment.com/
I asked about this on our last day at US (because I rented an ECV that day) and they said they normally have you take a ticket over there- BUT if they know the other park doesn't have one available for you (I asked "what if...") that they would escort you over with the ECV.
Hope this helps.
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