I want to finish a roughed in basement bathroom, it currently has a working sink. I want to move the existing sink left along the same wall 3.5 feet and install another new sink on the same wall 6 feet to the right of the current sink position. I can get the 1/4 inch fall on both sinks and want to tie them back to the vertical stack/drain the existing sink is tied to using a double T fitting. I would install a P trap to both sinks usinig a 90 degree elbow with a stub out to the horizontal. Is this O.K.

that would be fine. if you can try to use a larger size on the tee then your trap size. but that maybe very hard. sounds like you have it under control just fine.