Sounds like you're getting sea sick I have noticed that my Picanto is very sensitive to side winds. This is no surprise considering its shape (profile like an egg). However, my own experience is that my Picanto feels quite stabile until about 140 km/h compared to other micro cars.
Did you check out the pressure in your tires? If it's too low this may affect the stability, too.
Do you happen to use lower profiles such as 185/55-14 or 195/45-15? I know this makes the car feel more sensitive, too....
The Picanto suspension sometimes seems a bit uncultivated, that's true. But that's not neccessarily a small-car-problem. My brother had a 10/1999 Volvo 740 and that was twice as long and heavy, but in terms of suspension it was even worse.
I found that every car has certain speeds when all forces combine to make a big mess. If your Picanto seems too bumpy at 110 km/h try going a bit faster or slower. Mine rides very well from city speeds to 100 and from 130 to 150.
Anything faster raises fuel consumption through the roof, although I did have it between 170 and 175 km/h for quite a bit and it still felt solid as a rock. (Consumption: 7.7 liters/100km, usually 5.4 liters/100km)