I wouldn't explicitly mention it in the application, but leave this to the job interview.
Otherwise, you could write "Ich kann es mir auch vorstellen, als Teilzeitkraft anzufangen." (I can also imagine starting as part time employee), implicitly looking for a full-time job or "Ich wäre bereit als Teilzeitkraft anzufangen, aber suche mittelfristig eine Vollzeiteinstellung." (I could start as part time employee, but look for a full-time employment in the near future)
Don't make the error to go by priorities and write it like you posted, with the full time before the "but". Everything before the "but" is erased by it and you essentially just said that its fine for you working part-time, without the desire for a full-time employment. If you swap both options, you erase the part-time job part from the message and focus on the full-time employment.
Still, I recommend the interview for that. I am not sure if this is different in other countries (Germany usually is pretty special as I have heard in terms of job culture).
Maybe your wife doesn't know if the employer even wants a part-time worker at all or would not like her to start part-time (but rather allow her to reduce her work load after the company had the chance to see who she actually is). The interview is a two-way communication: She presents herself to the employer and the employer presents itself to her. It is the best part in the job application to find out what the employer really wants.
All the paperwork called job application has just one purpose: Let the HRD get interested in reading more after the first five lines and make the HRD feel like you are a great candidate after reading the rest and invite you to the job interview. As long as you didn't have to lie too much there, it is fine.
But the really deciding part is the job interview.