If I do traditional rental...I'll get about 15% CoC at $6K gross rents. 

Keep in mind the average person only buys/sells a total of 3-4 houses in their LIFETIME, and on top of that 80%+ do so using the traditional approach of buying retail off the MLS and having real estate agents hold their hands thru every step of the process.You, my friend, are a Wild West cowboy finding opportunity where others dare not tread. 

She had trouble getting more traditional financing take outs because of the type of markets she was in.

Traditional loan, hard money* refinance so i have no cash in the deal* Can i finance the house as a primary residence since my dad is living there and i have no other property? 

It's the same as a traditional Investment property from a bank.

Traditional financing on it doesn’t make sense.

I used traditional bank financing but was able to get them to allow me to put 20% down instead of the traditional 25%.

I'm primarily looking in Columbus, Ohio because I have strong ties to the area & a few relatives willing to help me scope out potential properties, they have many more duplexes available to purchase, and their market seems to be about where Raleigh's was ~3-5 years ago in terms of what you're able to get for my price range.I'm wondering if it would be better for me to finance the purchase of my new property with a traditional mortgage, or to use my inheritance & some of my savings to buy out my mom so I can take out a home equity loan to purchase a new property in cash. 

My question is whether I should pursue a short-term vacation rental property or a traditional SF home (or small 1-4 unit multi) for my first deal?

If you are obtaining financing, are you going through a traditional bank or lender or will you be using hard/private money?