What is their complaint and did they complain at the time when you employed your wife?
If you had the power to appoint her and your wife did a job for the company that the client was happy with then I don't see what the issue is. You can let me see the solicitors letter if you wish but I would resist any claim here, certainly from the narrative you have provided to me. Happy to discuss further. I hope that helps. Please leave a positive rating so that I am credited for my time.
There's nothing in company law to say so. It would be whether the company has any rules about authority when recruiting.
The other point is that if they didn't object at the time yountook her on and she did the job without complaint then you can argue that they acquiesced in her being appointed.