She could not find anyone to rent her a home because she was a stay at home Mom with no verifiable income/job (left job to move home). 

Dakoda, I would first recommend "The Ultimate Beginner's Guide to Real Estate Investing" by BP's Josh Dorkin, which is free on BP or Amazon.  

My usual approach is to find 3/1 or 3/2 single family houses in a good school district, but my budget will be rather low for this move since my family is staying in OH and we'll be running two households. 

Read books on investing in real estate, listen to the podcasts, attend webinars and stay active on the forums while connecting with other investors in your area and pick a niche.

Make sure to read the Beginner’s Guide: http://www.biggerpockets.com/real-estate-investing

We could stay where we are and refinance, using that money to invest.

Why would you stay in such a place for that long anyway?

Now may not be the best time to stretch for a deal and accept lower margins just to stay busy.

It sounds like the house is in great shape, this may allow for better rents-I always try to get high rent off of a fresh rehab AND I'm happy to wait for great tenants and/or tenants that are likely to stay for a long time.

Keep 1 bedroom available for myself to stay in from time to time?