In this position I don't like Bd3 much, but a case can be made for both Be2 and Bb3. I would probably choose Bb3, hoping to put some pressure on the a2-g8 diagonal somewhere down the stretch. But all in all, I don't really like white's position anymore. It's not bad in general, it's just that black seems to get the kind of play he has been hoping for.
To me the real problem is your moves 8,9, 10 and 11.
Ok, let's say Qc2 is probably fine, even though to me it's already a slight inaccuracy because it limits your options.
Now 9. Rd1 I just find weird. Question 1: what is your other rook going to do on either f or e files? Question 2: You know that black is planning for b5 at some point - why not put the rook on c1 from where it is prepared to put pressure? The other rook can then go to d1 for solid development.
If 8-9-10 are just inaccuracies, I'd say that 11.0-0 is a big inaccuracy/borderline mistake (I know I know, it sounds hilarious that castling in the opening could by a mistake at any point, but hear me out). Timing is absolutely essential in openings since it is so important to prepare your/prevent your opponents plans. Your king is not in any kind of danger and there is no need to castle right away giving away some precious time, especially because you KNOW what his plan is and you KNOW that you will be presented with the dilemma after dxc4 and b5. cxd5, a3 or a4 are all better than 0-0 IMO.
Basically, I agree that the dilemma in the position you've posted is not an easy one. However, with correct play and some preparation this dilemma should never arise, it is just a non issue. It's weird that you know what black's idea is and don't do anything to prepare/prevent it. If you don't like the a3-Ba2 idea there are still multiple ways to prevent this problem from arising.
Sorry for the aggressive tone of the post, I'm a bit cranky
Hope this helps!