If you measure everything out and it is square, then I'd box the connecting point differently. I'm not sure I'm crazy about the two frames sitting alongside each other, although they may be strong enough. The blunt ends are not pretty.
I would cut plates that will make a more gradual transition from the two frames, and add them to what you have. Grind off anything that's sticking up past the frame's outter edge, so when you add the transitions it's smooth. These angled plates will further work as gussets and enforce the area further also, plus make it look more professional.
Just taking what you have now and making all the square ends angle out at 45 degrees and boxed closed, will make it all look better, and be stronger. Do the angles on all edges, leading, top, or wherever there's a difference between the subframe and existing frame.