I am of two minds on this.
I guess my first question is, why do you want to be at BLT? And are those reasons more pressing than the extra space?
As others have said, it is definitely a small space for 4 people.
BUT
...it depends entirely on what the goal of this particular vacation is. BLT is all about location, and if you are planning to be out of the room (and there is a LOT to do in that area out of your room -- at BLT and CR, at the Poly and GF, and of course the question of how much time you'll be in MK) then it doesn't matter quite as much how big your room is. I've seen many people spend a lot of points on large units but spend virtually no time in them because they are at parks all day. Even if you have a non-park day, is your family the type to be at the pool from morning til dark?
We only have one child, but two trips ago we stayed in the BLT studio for 7 nights without issue because we are good at sharing small spaces, and we had that type of vacation. And for those reasons above, we LOVED being on the monorail loop.
However, if you do like to spend a lot of time in your room -- napping, preparing a lot of meals, watching TV, or whatever else, then yes, it might not be your best bet. When we take a trip where we are planning to be more resort/less parks, we usually opt for OKW for the lounging-around space.
That said, 13 nights is a looong time (for me, anyway) to be in one place no matter how roomy it is. If I were you I'd do just a few nights in a BLT 1-bedroom, and enjoy the things to do in the monorail resorts and BLT (and do your MK time while staying there), and then follow with some nights in an OKW studio at the end of the vacation to make up the point difference. And you'd still have plenty of room in that studio. And then focus on the other parks while you're down at that end.