Although your arrangements with your graphic designer may not have been very detailed I would argue that (if in fact it was copied) there was an implied contractual condition that you would receive an original design. From this you can argue that your designer has breached this condition and should put you in the position you should have been in if the condition had not been breached ie all the costs of re-branding or the license fee’s that the original designer is claiming. I wouldn’t accept as compensation the designer creating the new logo etc as they clearly can’t be trusted to do original work! Your other argument is negligence – the designer has breached its duty of care by exposing you to forseeable and expensive copyright infringement and the costs of re-branding if you end up doing this.