I can't see how the thing you show would add anything meaningful tothe joint. It might resist some twisting moment but basicly your welding strategy I believe is faulty and you will actually create a joint that is weaker by welding the two tubes to that piece inside with a wide bead, whereas if you used some holes so that you could do a rosette weld you could get some shared shear resistance.

Looking at the drawing of the frame member, you need to analize just what forces apply where---the power will be applied forward along the bottom rail at where ever your lower torque arms attach but they will probably be a couple feet forward of the axle so the joints shouldn't have anything but carry the weight of the rear portion of the body.