What a great start to your TR!

Sorry to hear you had such a rough day & it is a good warning to anyone, especially with LO's, to have a plan for if the room isn't ready. We are bringing our DD for her first trip to WDW in December when she'll be 15 months. We are also currently planning on staying in a Studio at a BWV. Hubby & I stayed there once before & loved it - although the mug refills there are a joke - the place you could get refills at the pool always wanted a tip...that got old fast. We've already agreed to not bother with the mugs this time.
Can you tell me what you like about a BCV studio better? We have been considering switching if our waitlist for a boardwalk view studio doesn't come through - I think the pool at BCV obviously looks awesome!
Loved all the pics - your girls are beautiful! Thanks for sharing the slideshow!
Um.... I'll do my best to explain, but a lot of it is just "liking it there", for no good reason - which I won't be able to convey very well I'm sure!

There are some "tangible" (obviously not, but I'm struggling for a better word this morning!) reasons though, which I'll try to remember.
The walk to the Marketplace from the villas is a short, beautiful one. Multiple times each day, neither of us minded going there for soda or coffee, snacks (pre-packaged and fresh, but a decent selection for sure), souvenir shopping etc. Obviously the "boutique" look of the stores on the BW versus one-stop shopping at the BC seems cute, but we know they carry almost exactly the same stuff, I personally would like to go to just one place (that is convenient to boot!) when I'm either ready to relax in my room or trying not to waste precious park time!
The lobby and restaurants and pool and everything else you'd want to go to that is part of the Beach Club/Yacht Club is all near one another. No walking down separate halls or elevators to get here or there, you just walk one direction and it's all there, eventually

We could get from one end to the other, passing everything, much quicker than we could get just about anywhere at BWV.
The pool is obviously no contest, and if it's not your thing then the quiet pools are exactly as beautiful and, well, quiet
The boardwalk is less than a 5 minute walk and a look out many windows, yet NONE of the "bustle" gets into your room when you aren't looking for it!
I hope that helps! If you have specific questions feel free to ask, because it's kind of hard to compare the two. I know I did, just because the proximity to the parks and the BW is huge to us, and they obviously share those things.
Have a great time planning your trip!