If I have a "moment" in a car I try to replay it in my mind's eye. What inputs did I make and how did the car respond?
There are ways to provoke a car into coming unstuck that will upset the most stable chassis but, IMHO, the Omega is pretty difficult to get out of shape unwittingly if it's all working properly.
So, I would say to the OP - have a think about the circumstances of the "moment" and try to figure out what inputs you made and how the car responded.
Braking, coasting, neutral throttle and hard acceleration during cornering will provoke different reactions from the chassis as will the difference between progressive inputs to the steering, brakes and throttle as opposed to jerky or panicked inputs.
Without knowing what the circumstances were it's difficult to blame driver, tyres, car or road surface, tbh.
However, if the car is suspected not to be behaving I would check tyre pressures and wear pattern first, give the suspension a quick once-over and maybe get it to WIM for an alignment before necessarily blaming the tyres.
On the tyre front I have used Michelin Primacy, Dunlop SP sport MAX, SP2000 and Conti Sport contact 3s on mine in 235/45/17 and all 3 have been fine from a point of view of grip in the wet. I found the Dunlops a little noisy, though.
Kevin