Hi Riu Girl and welcome to the Dis! Our first Disney trip with both children in tow was when they were 4 & 7. We rented a single stroller on the first day for our 4yo, and every day after that rented a double stroller for both of them. (You know how there are the fights you fight and the ones you choose to walk away from? This was one of the ones we walked away from, since our 7yo was very sulky about the whole thing).
They managed well in the stroller, except for the time at AK when I had to tip them out and make them walk for awhile because they were elbowing each other. They by no means spent the whole trip in the stroller, but we used it for those charges across the park to make a PS or get to the parade or make the trip around World Showcase in Epcot. It was worth every penny! The double strollers are particularly useful at the parades because you can park the kids right behind the yellow line and then park yourselves right behind the stroller.
DS and DD are both tall (95th percentile height for DS and 75th percentile height for DD) but pretty lean and they had lots of room. The elbowing wasn't due to lack of room, but lack of sibling respect! We didn't find the strollers too wide at all, but you do have to navigate with care in the crowds, of course. Also note that strollers aren't allowed in most lines or in some of the buildings at Epcot.
Unfortunately, I've been to Wonderland, but haven't rented strollers there, so can't compare.
I just wanted you to know that you should hold on to your stroller receipt, since if you hop to a different park, you can use the earlier receipt from the other park later the same day. Also note that if you leave the park at night with everyone else there's sometimes a huge traffic jam to get your $1 refund. There's no need to wait in a long line to get your refund. You can just park your stroller neatly near the return area and get your refund when you pick up tomorrow's stroller. Again, you need to hold onto your receipt.
We found 4 & 7 to be a good age for WDW. (and also 5 & 8, 6 & 9, 7 & 10, and in a bit 8 & 11). Who are we kidding? We're hopeless! We have such a good time together at WDW.
Hope you have a wonderful trip!
