Short answer is that what happens depends on the speed of the collisions, but at high speeds and head-on it should rather be a jet-like quasar than the supernova ejecta shell that we show. Still enough to destroy the earth if the collision axis is in the orbital plane.
http://link.springer.com/article/10.1007/BF00649946#page-1http://articles.adsabs.harvard.edu//full/2002ASPC..263....1S/0000004.000.htmlGetting the proper remnant body from such an event is part of something that I am actually working on presently. Perhaps sometime in the future we could create graphics to show a slightly more accurate ejection event.
Slow inspiral or accretion of two stars equivalent to our sun would not supernova. White dwarves are much more delicate when it comes to overcoming electron degeneracy pressure by reaching the Chandrasekhar limit and going type Ia, such that mere gradual accretion from a binary partner can be a trigger.
A head-on collision of a sun-like star in our own solar system is so unlikely as to be practically impossible, but in dense star-forming regions this sort of (near head-on) collision is now thought to be somewhat common and a source of some observed quasars.
To simulate such quasars/ejections accurately would require full hydrodynamic simulations of stellar collisions. At present researchers are still struggling to get sufficient resolutions for accuracy for such simulations on supercomputers. Universe Sandbox won't be able to do that anytime soon, I'm afraid. So accurate representations of ejections are a challenge.