*I helped my wife to do her homework - with the verb "to help" you usually use the bare infinitive (that is, you leave out the "to") so you would have I helped my wife DO her homework.
*I helped my wife to homework - "homework" is not a verb, and if it were, you would omit the "to" as I said above.
I helped my wife with her homework - this is fine, except make "homework" one word.
[not a teacher]
Student or Learner