ODD never napped in the stroller so an umbrella was fine for us. All great advice above, what's nice is you'll have several adults so you can also spell each other so you can go out late some nights without your grandson.
We just got back yesterday and even though ODD never naps at home, we were able to get an afternoon nap in most days if we were back to the hotel by 1 or 2. If we ended up staying later in the parks we'd go back to the hotel by 3, have a little pool time and then early dinner and early to bed. Either way is doable but I wouldn't recommend switching it up too much.
Oh, and MK and many attractions are LOUD. The last two trips we brought ear protection for ODD and she willingly used it on many occasions. It really helped keep her from getting overstimulated and cranky from the noise.
One last tip- work out with your daughter in advance what you are going to do as far as buying gifts etc. in years past we gave my DD coins - mostly pennies- and had her brings a coin purse into the park. Then if she wanted to buy something she had to contribute her own money for it, and if she was out of money, she was out of money. That helped her decide if she wanted something and we could always set the price very high or too high if it was something we didn't think was a good idea. The last couple trips we've gotten her into pin collecting (she can't bear to trade, but some CMs will just give away a pin rather than trade), and told her she can get one pin a day. Then if she really wants something else she can get that instead of a pin. She loves playing with her pins and telling stories about them, and showing them to people as long as she's not expected to trade them. Btw I wouldn't recommend a lanyard because the pins don't stay on through a 4yo skipping...