I think its the website owner who is the person you should go after as they are responsible for the content on the site not the designer.
The website owner can then go after the designer to fix the problem or get compensation for problem caused if the designer is at fault for copyright issues.
Legal stuff can be expensive and take time, my advice would be to (and record keep evidence) ask owner to remove content which is in breach of your copyright, give them a reasonable time to respond, if no response try and speak to them. If they are unwilling to address the issue then have your solicitor write to them, if still unwilling then proceed with legal action.
Of course we dont know all the detail so if damage has been done to your business then some more indepth legal action may be requirred.
The point is if it ever goes to court then you would be in a better place if you had made efforts to have it addressed without court action, could show the steps you had taken and could show you gave them the oppourtunity to put it right and had the evidence to back up your points.