Hi Matt,
Your trip is so close & you'll love the CB resort! I highly recommend a stroller for your 4 yr old. There is a lot of walking at WDW & your little fellow will get tired. My 5 yr old still loves being in a stroller & often naps in it. Its especially handy at the end of the day when kids are worn out & you're trying to get back to your resort.
The strollers available to rent in the parks are hard plastic & not very comfortable especially if kids are trying to nap. I would not recommend using a stroller rented in the parks for a 10 mo old. If you rent a stroller in one park, it must remain in that park. If you decide to park hop, you will have to leave the stroller in the 1st park & get another stroller in the next. You don't have to pay another rental fee within the same day - just save your receipt & present it at the next park's stroller rental location. If you plan to rent a stroller more than one day, you may want to consider a "Length of Stay" rental & save a little money.
If you are unable to bring your own stroller(s), I would rent from an outside source. Orlando Stroller Rentals has a big selection of strollers. They offer free delivery & pick up. Your stroller will be waiting for you at Bell Services at your resort & you can return it to Bell Services when you leave. Their website is
www.orlandostrollerrentals.com.
You will have to fold your stroller on WDW buses. Its a little more of a hassle to fold a double stroller but it may be easier during the day to have both kids in one stroller while one of you goes to get food & the other waits with the kids. Bring a bright ribbon/bandana to tie on your stroller so you can easily spot it when returning from an attraction to the stroller parking area. You'll very happy you have a stroller for your 4 yr old. Wishing you many magical memories!