The neighbor to my tenant is not being reasonable and continues to block parking access by parking in the driveway.

Her office is 2 blocks from Grand Central. 

Rent control is put into place politically by predominantly Democrats who think they're actually trying to help (or pander to their voting block) as a means of "protecting those who could get forced out by higher rents" I believe is what I've heard most over the past couple decades I've been at this.   

After about 3 months, we pick a couple days, and block the calendar.

Geographically they are blocks apart. 

Now the city has to plow to the new rear driveway so it was win & prevents neighbors from blocking access to it.

I see one block to the left prices are 100K lower then one block to the right. 

If you find you're unable to get something right away due to your credit or income situation, you may still be able to acquire your first place creatively via a lease/option, seller financing or buying a place 'subject-to' the existing financing, plus there's always hard or private money however either of the last two would require having 'take-out' financing lined up in advance, which might be a stumbling block.

Will they try to block.

I know firsthand that this can be a huge mental block, but the good news is that it's just that!