This $100,000 would be taxed at the applicable capital gains tax rate (0%–20% federally, depending on income) and subject to depreciation recapture at a maximum rate of 25%.

My first mortgage was almost 11% and that was a good rate.

But what I would point out to you is that the typical fee for property management is 8-10% of GROSS rent.

Good occupancy and solid CAP rate.

A cash out refi should take 2-3 weeks with most lenders, and you should have only an appraisal a credit report fee as upfront costs. 

I would also give her x amount of days to move but let her know you will have to charge a prorated fee per day after that to move for occupying both units. 

Although I will probably pay a slightly higher interest rate.

Reason is a Heloc generally carries a higher rate on a shorter term and "Can Never" be used as an "Asset, or for PITI reserves" which are both required when you buy an investment property. 

While I have a fantastic rate, the co-owner's giving me the option to refinance or he'll force a sale.

I can probably teach it, but I won't be spending that kind of money for the platform and I doubt people who wants to learn are willing to pay for the platform and tutoring fees.