"Mes enfants" should be acceptable too
No that's children not sons.
If a mother gives birth to two boys, she has two sons, or two children. It's the same. "Sons" is more accurate, setting the gender, but children is just as used in english, and fits perfectly in the sentence. I think it should be accepted.
why isn't 'gars' acceptable?
It is more familiar expression
what's more familiar than my sons though?
While you might be close to yours sons, you may not be close to whoever you're speaking with. A polite conversation in a formal register would require "fils".
Yes, this is true, but both sentences are valid in the sense that we're trying to learn the whole language.
As a rule of thumb, I always go with the formal register on Duolingo