Hi Bro,
Do the following, first of all again double check the wheel balancing of the car from some other good shop, and do let that person know about it before balancing that you already had a wheel balancing and the problem is not resolved. Also ask the person who is balancing your wheels to check that if any of the tyres is problematic or not. Some times the tyres get out of their shape and cause the car to wobble on some specific speed. Rims could have the same problem, so check them also.
As far as wobbling at the time of braking is concerned, mostly this problem is also becasue of balancing but if balancing does not resolve this issue and the tyres are also fine then you might have to go for checking the disc brakes, because if they have worn out or have become rough then they need to applied tool from some laith machine.
What Mr. Sherwani has said to change the place of the tyres, it is actually the same thing which I'm saying but its the remedy without diagnosis. You need to change the place of the tyres if your front tyres have got out of their shape and you dont want to but new ones. Then normally you put them in the rear wheels so that steering becomes trouble free.
Lets see what other experts say about this. By the way its a common prblem so you need not to be so much worried about it. It will be resolved. Cheers