Can I list the higher rent but then agree to a monthly credit for her managing the property or is it easier to have her manage building for free in exchange for rent?

As mentioned, the answer to that question isn't short or even terribly easy to explain.

However, after running the credit checks we found out that our credit scores are about 100 points different.

@Tony Mai Have you tried credit unions?

That's a terrible idea.

Our primary house is a fixer upper that I have been fixing little by little myself and over time that run into 25k credit card debt.

But if they have bad credit or eviction you can deny regardless of sec 8 qualifications as long as you deny every applicant with bad credit or a eviction You can turn away Sec 8 on the grounds that your properties do not qualify as you are not registered or had approval from the program. 

Some tenants may have some money but not the credit to qualify for a loan. 

Terrible idea.

@Dan Palumbo, sorry for being blunt, but this sounds like a terrible deal.