First and foremost, please accept my best wishes for a speedy and complete recovery! WDW is a great place to spend part of your recovery time!
I vote
ECV for the win; not only will it give you more independence & freedom, but you will be surprised - once you start paying attention - at just how much *walking* there is at WDW. The *average* visitor to WDW walks between 5 & 10 miles PER DAY.
Disney Springs alone is enough to wear a person out.
If you aren't used to self-propelling, you *might* make it through the first day on sheer adrenaline and willpower, but you won't make it to breakfast the next morning; your arms will feel like limp noodles. Sounds like you might need to rely a bit on other family members to help keep an eye on your sweet little girl, so asking them to push you in a manual wheelchair might not be as practical, either. Add in the fact that rental chairs are notoriously heavy, making them harder to push around, and all signs start to point towards renting an ECV.
Here's a few tips for a first-time ECV driver:
Who to rent from is very subjective. I recommend CALLING and talking to several companies, and see which one you like best. Prior to buying my own personal ECV, I rented from Walker, but that was several years ago.
Practicing your ECV driving and parking skills with the electric carts at Wal-Mart, Target, Lowe's, the grocery store, etc. will help a great deal. If you can tame one of those wheezing beasties, a mere rental at WDW will be a breeze!

Having said that, do take the time to practice at the Resort (or somewhere outside the Parks) with the rental, to familiarize yourself with how it stops, turns, etc.
Please remember that WDW has a rule - for everyone's safety - that only you ride the ECV. You will undoubtedly see people holding children on their laps while driving their scooters, but it's very dangerous, and I hope you will agree that your sweet baby girl is safer off of the
scooter.
Bring a brightly colored scarf, ribbon or bandana to tie on your rental scooter. It will help it stand out in a sea of similar units (if you park it to ride, eat, or shop a bit).
You will have to park the ECV in your room every night to charge it, so if you need to make a bit of space, ask for the table and chairs to be removed. You are not allowed to park it outside in a hallway or breezeway, or down at the lobby or bell services. (Pro tip: go directly to the front desk to ask for the table & chairs to be moved - don't call the "Front Desk" from the room phone, as that call goes to a Call Center for the Resorts, and not the Front Desk of the hotel you are at)
If the scooter has a key, always take it with you.
Don't be surprised if you park the ECV to go on a ride, or attraction, and it is moved when you return. The Cast Members are in a constant struggle to keep walkways clear and safe, as well as making sure that parking areas for mobility devices and strollers stay reasonably tidy. You will typically find it quite nearby, but if you don't, just ask any CM you see, and they will help you find it.
Remember to stay sharp and focused while driving the ECV - people at WDW tend to be doing everything but paying attention when they are walking, and many of us here have had folks run right into us, or walk right in front of us as we are moving! I try to make eye contact, smile politely, and offer an cheerful "Excuse me!" when needed, but know that you WILL at some point find yourself nearly running over someone who is either texting, taking a "selfie" or posting their latest selfie to Instagram.
Probably the hardest thing you will do with the ECV all revolves around dealing with the buses. Make sure you are parked in the white painted rectangle at the bus stop (unless another guest beat you to it) so that the driver sees you, and knows you are waiting to ride.
When the ramp comes down, line up on the ramp, and try to go right up the center. At the top of the ramp you will typically have to turn a bit to the right. GO SLOWLY, especially until you are used to the ECV. Even experienced users take this carefully - the last thing you want is to run over the driver, or hit the side of the doorway going in. Important to know: the drivers will give you instructions and will help as much as they can, but it is up to you (or a member of your party) to actually get the ECV up into the bus. You will always board first, and exit last. Your family can walk up the ramp and board behind you.
You can take the ECV on all of the boats (except for the smaller launches) and the Captains have a portable ramp you should be able to use. It is identical to the ramp they will use for you at the Monorail stations.
Finally, a few quick driving tips: anytime at WDW (or anytime using an ECV for that matter) be aware of ramps, hills and slopes. Going up, you will want to lean forward to help shift your center of gravity towards the front of the ECV. Take your time on steep slopes, hills or ramps, and if possible, approach them at a slight angle at the base.
Coming down, be very aware of your speed, and make sure you can brake effectively. This is not the time to try and drink your Starbucks; two hands on the wheel!
When crossing the train tracks embedded in Main Street at MK, be sure to cross at an angle. Otherwise, you risk the wheel(s) getting caught, and you could find yourself dumped on to Main Street. Everyone wants to have an unforgettable trip - just for the right reasons!
Have a Magical trip - and remember that your scooter is just a tool to let you keep up with your beautiful family, and have fun!