After you've completed the work, you will likely have increased the value of the house so you'll have some forced appreciation.

Do you think this is positive for a rental investor as higher rates may make ownership costs higher for some buyers thus increasing rents?

I would try to find a more year round type vacation spot so that you can decrease your vacancy rate and ultimately increase your profits.

During the rehab, I would add the 3rd bedroom back which would increase the value.

The home currently has a tenant and they want to stay he’s warned then of the possible sale and that within a few months I can increase rent to $800-$850.Taxes are $1604 a year and insurance rings in at $650 annually.

I will say at least for me, I wouldn't assume 4% increase in income though. 

Any work that you do, and subsequent increase in equity, is YOURS. 

A 10% cash on cash ROI could be slashed with a single percentage increase in interest rate.Secondly any mortgage laws, requirements, etc. that may change or negatively affect your property can be mitigated.

I actually predict a influx of rentals of the sell market next year, when the new landlords of the current and past couple years realize the promised cash flow is nowhere near expectations, their property taxes have increased 30-50%, and they actually have to put money in every year.

I want to increase cash while building a positive asset portfolio.