A copy of the credit card front and back should be in your wallet whenever you visit a restaurant. This is the first piece of information that a restaurant wants to see. They may also want to know your exact plate number so they can order your meal exactly to your preference. They will also want to know if you have any carry-on-sized luggage.
However, that particular copy of your ID may be of the highest importance to you. You don't want to leave home without a copy so it is vital that it arrives quickly after your reservation. As long as you send it with your check along with your payment, the restaurant should be able to have it no problem. You could even have the copy sent to you by an employee at the restaurant, who will then keep it in the safe for your future reference.
A copy of your ID should always be kept at home. It is easy to steal if someone knows that you have that particular ID. It would be easy for a burglar to get into your purse or wallet and grab a hold of it while you are in the kitchen. That is why you want to make sure that your copy of credit is kept with you as well.
You should not wait until you return from your trip to make sure that your copy of ID is in its proper place. If you leave it at home, it is easy for someone to steal it right away. You want to make sure that you have it with you and ready to use when you need it.
Even if you have a copy of your credit card with you, it doesn't mean that you should leave it in your hotel room. Your hotel room might be a nice place to stay in, but it is not secure. Anyone could walk off with your card and run.
There are many other things that you want to do to make sure that your own copy of ID is safe. You should always carry a copy with you at all times. If you go to a restaurant, ask for a copy of your ID before you leave and make sure that you have it. This will not only help you at the table, but it helps you when you are about to go home.