Hi Goncin
I think "your history of defeat and pain" would be better as you suggest. (Then you can use the word "again" at the end of the last line of this first verse in order to recreate a rhyme.
Are you sure it is "had" and not "have" in first line of the second verse? Also the verb is "choose", not "choice" in the last line(I've edited this one already. The third line is a little bit difficult to understand. Do you mean "I know everything (there is to know) about you?
This could give something similar to:
"I'll change your history
Of defeat and pain,
To give you a new heart
Full of victory and love again!
I know where you have wandered;
I foresee your future, I know your past.
I know all there is to know of you;
You're free to choose your Way at last.
Your mistakes, I can correct;
Your sins, upon the cross I paid;
I came and restored your heart
So that, in your mission, you will keep faith.
Bises
Tantine