For car hire, if it's not included in your package, you can try the usual car hire companies:- Hertz, Budget,
Avis, Dollar. Alternatively, we have successfully used companies like: USRentacar and Holiday Autos. You really need to shop around to find the best prices.
Strollers can be rented at the parks - they are quite pricey, though.
You can get a 'Length of Stay' rental where you pay a one-off payment for the number of days rental that you need. When you visit a park, show your receipt at the stroller rental place and you will be directed through the queue with little or no wait.
From Allears:
There is a slight discount when purchasing the Length of Stay rental ticket. The Length of Stay option is NOT offered during peak attendance times, however, such as Christmas.
Disney
stroller rentals costs are:
$15 per day - single
$31.00 per day - double
Multi-day rate:
$13.00 per day - single
$27 per day - double
Another option is a stroller rental company
www.orlandostrollerrentals.com although I haven't used them myself so can't vouch for how good/reliable they are and not sure about the costs - although I know they're significantly cheaper than Disney.
Are you staying in a villa? I know that many villas have strollers available for use while you are staying there.
A final option is to buy a cheap stroller at
Walmart or other supermarket and use that during your stay.