It is wrong. "Sein" has to be in the last place.
Word order in German when there's a modal verb: Subject (ich) - modal verb (will) - everything else like what, when, where,... (ein Vater) - verb in infinitive (sein).
"I" and "father" are still talking about the same person. Yes, father is a predicate nominative. If you said "I want to have a father.", then "I" and "father" would be different people and "father" would then be the direct object.