How do eradicate pad to pad clearance with-in the component in Eagle Tool?
The last version of EAGLE I used has a sticky 'accept' button when running the DRC, after that further DRC runs will ignore them.  

I can't tell what your dimensions are, but as far as the DRC rules settings, the pads would would be in the clearance dialog with the pad / pad row/column setting make sure you are using the correct units.

That being said those inter-pad distances look really tight (no scale to compare to, but given the labels I'm thinking 2.54mm or 1.27mm spacing).  Don't forget that even if the board house can make a 3mil spacing board, the fact that you may have to solder pins in and accidentally bridge them during the process may create difficulties.