"Every direction" isn't what you think it is.

Even if we had a voyager travelling the "opposite" direction, once outside the solar system they'd appear to be travelling at almost the same speed with respect to the orbit of the solar system around the milky way.

The solar system is estimated to orbit ~200km/sec around the centre of the milky way.

Even with a perfect ejection, at the estimated speed of Voyager you'd end up with one probe going ~180km and the other ~220km, which isn't a huge difference.

And that's without the fact that getting Voyager to that speed required some unique planetary alignment.