My question is regarding Qasr Namaz. If I intend to travel to a city where Namaz is Qasr and I intend to stay for more than 10 days. But I intend to travel back in the mid week and go back again. But my total stay there would be 10 days with a break of 2 days. Whether my Namaz will still be Qasr?

To pray full prayers, you need to stay 10 continuous days, with no break in between.
In your case, your prayers are Qasr, during the whole period.