Before you think I'm a nutty person butting in (well I am, but not just that); also have EDS so know what I'm talking about.
If your arms and/or shoulders are in such a condition you could not use an ECV, using a wheelchair is not even close to realistic when expecting any independant mobility. Renting at WDW would not be a smart thing, but there are more then plenty options out there, including in the rental market, that demand minimal of the arms and/or shoulders compared to a wheelchair. Apart from the ECV caracteristics themselves, adjusting the settings of the ECV would be the other most important thing. To give you an idea; on can safely operate an ECV while fixing the arm and shoulder by keeping the upperarm against the chest and while no need of range of movement or angled usage of wrist or thumb etc. As long as one can move the underarm and fold some fingers, there are ECV options out there that can be used.
Other than that or being completely dependant on your husband to push a wheelchair options could be a rollator (walker with seat) or powerchair. Where the latter would not be an option for you as you are not an experienced user, as I understand it. Those things are a lot more intricate to use than an ECV and thus tend to not get rented out unless one is an experienced user. And honestly personal opinion? VERY wrong option to start using one at WDW for the first time. It does take a lot more practice to get the hang of and a WDW trip will not be the place to do it (unlike an ECV it does not take minutes, but days or weeks). Because of the sensitivity of powerchairs it is very easy to not have perfect control over them when not being an experienced user. Huge risk of accident waiting to happen. Even if we were to disregard all of that; it is very energy consuming to start using one for the first time and can drain one out. Combine that with WDW where you have to have eyes in your back and hundreds of folks running around. A day at the park will drain. Even for us experienced users that have perfect control over the chair it can take a lot to constantly be on the look out to prevent collisions as people have no clue how these things work.
Sitting on lap? Would not advice it at all. Not only does it come with the risk of her moving and that causing pain or (sub)luxation for you, but you will fool the body and run risk because of that. The added pressure of DD on lap gives the body a false sense of more stabilisation. It will respond by relaxing more. This will not directly disappear when DD gets of your lap. The effect will linger on and can result in stuff giving way earlier than you are used to normally because of the body being still more relaxed.
Can't judge your walking abilities, so can't say anything about the rollator being realistic for parks, airports, just resort or not enough for one or all. For a moment assuming that isn't an option, I'ld personally start investing in ECV-searching. Not waiting until the trip, but starting today. Try out rental options in your area and work from there. Find out what might be pain points and what not and go from there. Time has a huge benefit that you can tweak things to fit you personally. And again; changing settings of the seat, stearing column (both distance, angle, height etc.) etc can make or break something as an option. And I'ld keep at it if need be, can sometimes take multiple ECV's before you hit the right one. To give you an idea; my arms and upper body have been my biggest problem area for years. Still I have used an ECV for years without problems and had to change out of it to a powerchair because my walking went from small distances to none, needing to use a poweroperated option inside -which obviously an ECV is a pain in the home- and needing such support from the seat it was not possible on an ECV. Own creativity can also add a huge difference to making an ECV from "mwah" to "yes, I can do this!". When hitting the right option; rent it at home, tweak if need be and change the setting to fit you and bring it along on the trip. You can bring it along free of charge and does not count towards your baggage limit. Simply inform the airline of it.
I know it's not the most loved opinion on the DIS, but a 5 year old should be able to do the walking to such an extend a stroller or lap rides should not be needed. Simply be aware of the fact she is a 5 year old. Regular breaks, a bit of smart planning (varying quick rides with shows where you'll be sitting for a long time and thus feet getting a break anyway), midday break and she should do fine. But then again, I come from a place where it is still the norm that kids "obviously" walk these distances on days out and other moments, including multiple days, when reaching the age of 4 or 5 and it being "obvious" to pace to include them. Not in the last part for us adults either ;-) as keeping their pace tends to make it a lot nicer on adults alike and enjoying things as kids experience them ends up always being that bit more magical than how we adults tend to run along, run, run, run, keep going and end up missing some of the smallest unexpected but most special thing of the day.
This is a genuine question, and I have no idea about policy or even whether it's safe. 
. We're flying out of a small airport here so no concerns there.
fellow bendy! my thumbs are one of the worst...they sublux inwards. I just had my wrist fused and so far it seems to have helped with the dislocating of the carpals..
