"I was willing to do whatever was necessary to be the wife he wanted."
"I was willing to do whatever necessary to be the wife he wanted."
with or without "was" make a big difference?
It does make a big difference, and in this case, it is necessary to increase "was"; you referred to a past action in your statement, which means the rest of the sentence referred to that action must be in the past tense. When you have doubts related to this stuff, try to read your sentence out loud, it shall sound weird, since you are referring to an action in the past that has no involvement with the present.