Apartment is being sold, charging higher rent?

My 4 year old daughter, fiance and I live in a duplex owned and occupied by my fiance's grandmother. She charges us only 600 dollars a month because she knows we can't afford much more. Well we rexently told her that we are going to be moving to florida (we live in rhode island) in october or november because we can't afford another winter here. We told her that the reason we're not leaving now is because we need until late fall to save up enough money for the truck rental, security deposit, etc. Well she called up an old friend that she knows is interested in buying more property and asked if he wanted to buy (we think she did this out of spite, she does spiteful things rather often). Apparently he does want to buy the house, and may be buying it literally this week. We have already been informed that he is going to be charging 1500 for rent, and that if we can't pay it then we need to leave. We have about 50 dollars to our names, and have no current lease since it is the grandmother that we rent from, and she didn't see fit that we have anything protecting us. Can the prospective new owner really just come in and say get out with no notice while we have a small child, nowhere to go, and no money for a new apartment?