I will try to answer your questions succinctly. The outcome can vary from one insurer to another but generally...
Adam, if a stranger damages your car and you claim on your insurance but do not have any details of the person responsible, then the insurance company will not waive your excess and the claim will likely affect your future premium. This is because the insurer will bear the full costs as no recovery is possible. So although you are not at fault, it is treated in the same manner as an at fault claim. If you can and do provide the details of the stranger, then your excess will be waived and the claim will not affect your premium, regardless of whether the insurer makes a subsequent recovery of costs or not.
If it is your mum who caused the damage, the law says that the insurance company, after paying your claim, cannot recover from her. However if you provide her details to the insurer, it is likely the insurer will waive your excess and not increase your premium. This is because they are bound by the policy wording which says this is what happens if you are not at fault and you provide the required details of the person who caused the damage.
If you try to prevent the insurer from seeking recovery from a stranger, then the insurer, relying on the clauses Jack has quoted in his last post, can refuse your claim entirely. So you cannot gain any advantage from such a tactic.
Jack, you do not need to be concerned about giving your recovery rights to CGU. Statute Law, in this case the Insurance Contracts Act, overrides anything the insurance company puts in the policy wording. CGU cannot recover from your mother.
The bit about not covering family members is in that part of the policy dealing with your liability to others. That is where you for example, driving your car, damage mum’s property. If she was someone living with you then you are not covered for the other property damage. This is like the other side of the coin to the insurer not being able to recover from a close relative.
I am confident you can claim for your repairs, provide your mum’s details (making sure they understand it is your mum), not pay an excess, not have your premium affected and not have CGU chase her. My only slight doubt is in respect to excess where the policy clause says you must also provide her insurance details. They may try to put their own interpretation on this to mean they only waive the excess for insured third parties. But let’s not worry about that until it occurs.