The Beach and Yacht Club is such a special place, great access to two parks and monorail access to MK if you want as well.
Just a short walk thru Epcot( grab a snack or adult beverage on your way) and hop right on and it takes you to MK
According to google maps, it's 1.4 miles walking through Epcot. I'm 47. I know I can do it. I know my kids could do it but they'd be done for the day; we'd have to use a stroller. My wife could do the walk but as she comes from pale pasty Scottish stock, if it's even a slightly hot or humid day (heat and humidity? IN FLORIDA?) by the time we got to the monorail she'd be a beet-red human puddle. My mom, almost 80, could not handle the walk, period.
I don't know the energy level of the OP's grandparents - maybe they're very fit and would enjoy a nice walk first thing in the morning, maybe they have scooters and the walk is moot. But if you're planning on going from BC to MK in the morning, it would have to be a morning epcot's open early enough (or you leave later in the morning). If you're planning to return that way, bear in mind, you're talking about a half hour walk AFTER all the walking you've done during the day, and for people who are very young, very old or not necessarily that fit, a 1.4 mile walk on top of all the prior walking might be too much.
As for hopping on, again, it's not like the monorail is waiting for you and refusing to leave until you arrive. Depending on time of day, there could be a line, or you might miss one and have to wait for the next one.
If you're staying at BC I'd only recommend monorail to/from MK on a park-hopping day - walk to Epcot, spend morning there, monorail to MK for afternoon/evening, then bus back. Or bus to MK, spend morning there, monorail to Epcot for afternoon/evening, walk back to Epcot.
I'll chalk up the comments about the VAK being bland & boring with "nothing special" food as a different strokes for different folks kinda thing. I do agree that the resort is quite huge and spread out, but it's also lovely and a great resort to explore and savor. Stormalong Bay is a superior pool, and between BC and YC there are 3 more quiet pools, but Animal Kingdom has two very nice big pools as well as an amazing kids' water-play area any kid will love (I'd also add Stormalong Bay might be a better pool for a different trip when the OP's child is older; at "almost 3" the pool might be too huge and spread out, and the slide might be more terrifying than inviting). Since the OP mentions probably renting a car, I'd recommend, if the Animal Kingdom is the choice, using the car to get to all parks except MAYBE MK, depending on how much the kid likes riding the monorail. If it's BC, you still might want to use it to get to/from AK
Also, to the OP - were you thinking about trying to book a single room for the 5 of you? Or a 1BR Villa? Reason being - the 1 BR Villas in the Kidani Village have a second bathroom, and if you're a party of 5, that might come in incredibly handy. And at Animal Kingdom, you will have a much better chance of getting such a room because it's so much bigger.
Both resorts have amazing pros - BC might have more pros especially when it comes to location, not just to the parks but to 4 other resorts with their dining options, to say nothing of the dining options at World Showcase at your "back door." But VAK is awesome, a truly unique resort if you intend to spend some time actually enjoying the resort, and if you do need that second bathroom, no contest.
I would not recommend you consider "monorail access to MK" as a plus for BC, unless you think your party has the stamina to include a nearly 1.5 mile walk on top of the walking regimen a WDW trip requires in the first place.
). The boats to and from DHS would be fun too, and if she does fall asleep in a stroller you could walk around Crescent Lake and look at the Boardwalk area. 
