Honestly I too think the direction of the gate should be so it swings into there own property , WHY dont you check the links above to find a real estate atty to do a letter for you telling them that the direction the gate currently swings is going to cause your fence to be damaged and they should change the direction of the gate swing so it swings into there own property or your only recourse would be to sue them for damaging your property , This of course comming from a atty they will either comply and like you less
OR they will not comply and like you a lot less when you sue them for the damage done and the share of maint cost to the road they wouldnt pay
~~~ Either way since it appears you dont care if they like you or not go for it , pay a atty to do a letter for you and wish you were a mouse in the corner getting to see and hear lots of bad behaviour & verbal agression when they get the mail opened!