I am not aware that either steel or nylon is weaker in normal use. There might be something else wrong. Do your strings always break on the same end? The peg end ? The bridge end ? Look for any sharp edges that might break a string. Another way to break a string is to make it too tight. Are you sure of your notes?
Yes, strings can make a big difference in sound quality. Most people now use nylon strings. Many distributors will sell just an "E" or "A" string or both, if you want a less expensive way to test other strings.
When you come to a fork in the road, take it.
I have an online tuner for you to check that you are not tuning too high.
Click here: ONLINE VIOLIN TUNER
The quality doesn't depend on the string type but can be very much affected and improved if you choose the right one.
I saw Dominant strings set from a reliable music store near us and it costs 2,500 pesos which is almost a half dollars. Is it the normal range of Dominant in the market? because it is too costly in peso. thanks