Any Personnel experts out there?

Okay. My belief is that it would only be an ethics issue if her father was lying.

A sick note (whoever signs it - provided it is a doctor) is simply proof that they were sick -you have to accept that

but

you don't have to accept continuing or repetitious 'sickness' if it is destructive to the company - this comes under 'capability'

It is suspect though why not call the BMC and see what they think

If her father is her GP there is little you can do about it except counsel the member of staff for sickness, at the end of the day a GP note is a note, it doesn't matter who the GP is

A sick note is quite binding, but if they are off for more than say 6 weeks, you can insist your company GP sees them (many will do this but it doesn't comne cheap). If they state they are fit to come back to work then their Father, even as a GP, will probably not put his reputation on the line to keep her off sick unless he is convinced the claim is valid and your GP missed something.

I was under the impression that GPs weren't supposed to treat their close family.

You are legally obliged to accept the sick note, but ethically this is very dubious.