Hello Melissa! Thanks so much for your question. It sounds like you are trying to find what would be the best option for both your child and mother in law. I won't have an answer for you, only you can decide which is best, but I can help you go over each option.
If you go with the stroller option, you won't be able to take it through the attraction queues. All attractions (with the exception of Kilimanjaro Safaris) have a stroller parking area located outside of the attraction entrance. If you are still considering a stroller, I suggest that you buy a cheap umbrella stroller and bring it with you. It will pay for itself if you plan on staying in the parks for over a day, and you can use it while walking to and from bus stations. If you rent a stroller within the parks they will not let you take it outside of the park, even if only to the bus stations.
The parks also have the option to rent
wheelchairs or
ECVs (Electric Conveyance Vehicle). My mother usually rents an ECV and it works out well for her. You can take ECVs and wheelchairs through attraction queues, and when you are about to board the attraction you will go to the wheelchair/ECV entrance. There is a website page that details the
attraction access categories so you can plan accordingly.
In my knowledge there is not an option to rent a walker through Walt Disney World. However, you can bring your own, so if your mother in law owns a walker she is more than welcome to bring it.
I hope this helps and if you need anything else, please stop in and ask. Have a magical day!