Third Party Mandate - Nightmare!

It is perfectly OK for any relative to witness a will, as long as they are not a beneficiary.

So if my mum witnesses me doing a will, will the courts accept it?

You need two witnesses and you must make it clear in the will that you are leaving nothing at all to your mother. If she would normally be the main beneficiary then it would be a good idea to explain in the will why you are disinheriting her. If you then die before your mother, the two witnesses may well be interviewed if the probate court thinks it is suspicious. But this is not legal advice! Go to a solicitor if you need that. I think it’s a bit odd to use your mother, but that’s just me.