Mine squirms around all over the place at times, especially over lane markings and seams in the road surface. I put it down to the tyres, or rather their tread pattern.
When I first got it, it was fitted with Bridgestone Potenza RE050A tyres and holding on to the steering wheel when changing lanes or braking was like trying to keep hold of a wet eel
. Following the suggestions of others on previous threads on this 'tram-lining' effect that this was down to the straight cut grooves around the circumference of the tyre following the ridges in the road surface, when it came time for new rubber I put on a set of Vredestein Ultrac Sessanta which have a chevron-like tread pattern and the improvement was immediate and like night and day - she felt 'planted' no matter what you were doing. The other 'plus' was that they were a good 15% or so cheaper than the Bridgestones.
Unfortunately, thanks to a local builder's inability to keep his stock of roofing nails away from the surrounding roads
, I 'lost' 2 of these tyres after only a few days and another 1 soon after. As the Vredesteins were not a stock item with my local tyre depot and had to be ordered-in specially, I've ended up now on a set of Pirelli P Zero Nero (I had to change the last remaining Vredestein to keep them all the same), which fortunately the builder (or his insurance) has paid for. The down-side is that these have straight-cut grooves and the tram-lining is back with a vengeance!
I can't explain why you only felt it changing lanes in the one direction unless the under-inflated tyre had something to do with it being more obvious on one side than the other.