There has been an increase in the number of specialized stores who ...
「こだわりの…のお店が増えてきた」は次のように言えるかと思います。
ーThere are more and more specialized shops who ...
ーThere has been an increase in the number of specialized stores who ...
「こだわりのお店」は specialized shops/stores のように言うと良いでしょう。
例：
There are more and more specialized coffee shops who measures the amount and temperature of the hot water they use.
「使うお湯の量や温度を測るこだわりのコーヒーショップが増えてきた」
ご参考まで！
カナダ 
