Does this sound like suspension issues

New (to me) 325i convertible - 1994.
Had new tyres and tracking just done.
On smooth tarmac - car runs straight and true - no issues.
Start to put it onto slightly older/ repaired tarmac and it vibrates a
fair bit with a bit of vibration through the wheel and side to side roll. Not like on a ship where the body would roll slowly but a lot of sharper knocks coming from all angles.
Hit some potholes / cats eyes on the road and you feel it through the steering wheel and through your backside - like a thud/boot up the arse!
Just went over some sharpishly high and triangular shaped speed bumps and the body appeared to be flexing all over the place, passenger and me nearly hit heads we were getting chucked about that much :) This was VERY slow speed.
Seriously though, I get the impression that at speeds over 50mph on dodgy roads the car needs to be held onto as opposed to driven easily...
Before I hit a garage who undoubtedly tells me I need to spend thousands, what would you say most likely culprits were.
P.S Have a receipt from the dealer ( non BMW) who had it serviced at BMW pre me buying it and the invoice says they installed dampers. They also put in a second hand shock back left that he supplied to them. Getting new parts in NZ can be very costly.
Thanks
Ged
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
What tire size, brand ? Handling is rather hard with large and low profile tires. Can be a PITA on badly repaired roads ! Mine (Z3 coup 3.0i) did that since the very beginning. 225x45x17 FW & 245x40x17 RW . Had it verified twice @ 35000 & 70000 km. Everything was perfectly within the manufacturing ranges. I think that the tire brand, dealing with the temperature is of a first order in the withstanding. It seems that with the Dunlop the car was smoother than with the Potenza S03 Bridgstone which seem to be made from a harder rubber.

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Tires were Michelin - Bloody expensive ones apparently that needed changed.
Now have Goodyears 205/55 R16.
The problems were the same with the Michelins.
I am taking the car into a shock specialist centre. They apparently stick it onto a rolling road and some computer rattles the wheels up and down and measures your shocks for wear and tear etc.
Thanks for your help
Ged
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Motorsforum.com is a website by car enthusiasts for car enthusiasts. It is not affiliated with any of the car or spare part manufacturers or car dealers discussed here. All logos and trade names are the property of their respective owners.