SHOULD I REMOVE THIS TREE?  Why or why not?

Ok, so I have this rather large tree (4-5' diameter) in front of my SFH property. It sits about 3' in front of the house. THe shade from the tree actually prevents grass from growing under it so the area right in front of the house is bare or grass and is just dirt. Additionally, the tree drops ton of sap unto our cars since our driveway is right beside it. Now, my wife and I are living in the property for only six months and then we will be turning it over into a rental property. The tree bugs the hell out of me and I want to cut it down but the other part of me is saying save the $ since this is only a temporary stay for a few months. The removal and stump grind is $1900 (market rent of the house is $700). That price tag is another factor that makes me pump my breaks.

I wanted to ask here, based on others' experiences, should I just go ahead and remove the tree?  Simply for the reason that I hate how it looks and to prevent future problems of it…or would it not pose too much issues in the future and I should just deal with it until I move and rent the property?  Attached are pictures of the tree.  

Additionally, would the removal of the tree add value to the house?  

And (off tree topic), would a fenced backyard add value as well (quoted at $2K for install)?  

I have recently repainted the entire exterior of the house (pictures are post-paint job) as well as replaced the roof. 

Thanks for the help! Sorry for the long read. :/