Matthew, there is lot's of good advice on this thread, and some of it is better than others. My father passed in 2012 and left us some property but I was already in the business so that was not the problem. My father made some wishes known regarding the property that my sister and I decided NOT to keep because it was NOT financially sound. We did NOT dishonor him by not following his wishes. Without going into a long story, my parents made a complete MESS of their estate that took us over three years to straighten out. My father had Alzheimer's for 12 years and for the first 6 of that, he was making some really poor decisions but no one wanted to tell him he was wrong.
Anyway, here is the way to look at this situation. You have a property, let's say that it is worth $500,000. That property will require annual property taxes, insurance, upkeep, management and other miscellaneous expenses. Using just a round number, let's say it cost $1,000 a month to maintain the property, not doing any Capital Expenditures. At the current $1,400 a month, you would net $400 a month, or $4,800 a year. Currently, a 10 Year Treasury Bond is paying 1.77% and you would receive $8,850 a year on that $500,000. This is why everyone is posting that you are LOSING money, because much simpler, much LESS of a headache investments would pay a LOT more. Now let's say you raise the rent to $2,500 a month and still spend $1,000 a month on expenses. Now you make $1,500 a month or $18,000 a year. This beats the 10 Year TBill but is still only a 3.6% return on your capital.
No one on Bigger Pockets can tell YOU what is BEST for YOU. We can only tell you what WE would do if we were in that situation. I WAS in that situation and sold the property, and more than doubled my monthly income. But, that was best for me. My father had a $500,000 house and was only getting $3,800 a month for it and I couldn't sell it fast enough. I turned it into over $8,000 a month income. (in California on the sell side)
My best advice to you would be to do very LITTLE the first year. Make sure the house is in good shape and LEGAL/SAFE. Let the tenants know that you are the new owner and that any 'agreements' with your father are null and void. Be professional and kind. Charging market rent is NOT evil or immoral. You gave them notice and now you should follow through with it. If you do decide to re-rent it, I would suggest a one year lease. Don't sell, don't refinance, don't do anything drastic. Take the time to learn more about real estate. Read about what kinds of deals and how they were done here on Bigger Pockets. Read about strategies. Learn different avenues of real estate investing. Find a top Realtor in your area who is experienced with working with investors. Find a Real Estate Investing Club and go to some of their meetings.
You have a great opportunity here and the worst thing to do is to make a 'rash' decision. Take your time, learn as much as you can and then create a deliberate plan.