We can't really answer what he has to prove to show that you are unfit, other than your are incapable or unwilling of providing proper care and supervision of your children. Beyond that, it's too much of an open question with endless possibilities.
With that said, the standard for your husband to obtain custody is not that you are unfit. Even if you are a good parent he can still be awarded custody as long as he is able to show that it is the children's best interests.
Your children are important, so you do now want to gamble on custody without assistance.
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