Переклад - Боснійська-Англійська - ja dajem svoju suglasnost da moja zena moze sama...

It is a part of written statement for getting permission for the child to leave the country only with one of his parents (in this case only with his mother).
As I think there must be blanks for the names of father, mother and child..(and for numbers of their internal passports or identity cards..

Misspelling: "traveling" and maybe it should be "trip".

I consent to my wife traveling with our son

or

I give a consent to my wife to travel on her own with our son

What do you think about: "I consent to my wife's trip on her own with our son."?

I think it's fine...