The loan officer says the refinanced amount would be 75% of the purchase price and not the new appraised value after rehab.In this case, is it a bad idea to transfer ownership of the duplex into my family member's name and then purchase the duplex back but this time financed? 

Be prepared to transfer title back into your individual name before refinancing the loan.

This helps avoid issues with lenders when refinancing down the road.

Is this due to a concern that the investor might actually be refinancing and making a NOO into a primary?

I had cash flow left over, and after 18 months, we refinanced and I paid back the HELOC.If you can get into a bigger deal that will create more equity, then it makes sense.

Once you reach greater than 20% equity in the property, it would be a good time to consider refinancing so you could eliminate the mortgage insurance with conventional financing. 

Refinancing?

Wondering if there are DSCR options for 2nd mortgages where can pull out for example just $100k without refinancing the first mortgage?

That generally means buying cash, doing a rehab, and refinancing.

As far as $12,000/year in cash flow if that was your only metric I’d say that makes sense because I have a similarly priced SFH I own in my market that before I refinanced it was cash flowing about $950/month.