There are several ways to answer this question. If we are talking about one specific isolated moment in the past , i.e this one childhood memory , then lets use the simple past.
The words "in my childhood " are not very common in the English in spoken language."When I was young(er)" or "One day when i was young" sounds a little better. Therefore the first sentence should be:
"When I was young , I went to the swimming pool to learn how to swim with my brother.
Again , there are several ways to tackle the second sentence. Lets conjugate the verb take into the simple past , i.e " took".
The words "But" and "until now" need to be corrected. I suggest replacing "But" with "although/even though/nevertheless " , and "until now" with "until then/ Until this moment/Until this day". So lets look at the second sentence:
Our trainer took both of us into the deepest part of the swimming pool, even though my brother had been scared of swimming until that day.
Although my brother had been scared of swimming until that day, our trainer took us into the deepest part of the swimming pool.
Until that day, my brother had been scared of swimming , nevertheless our trainer took us into the deepest part of the swimming pool.