Cannot understand what your issue is.
You want to pay your bill.
You want it sent to your address (I assume this is already happening).
Your wife is going to pay it.
Simply make sure the billing address is correct, Make sure your wife pays the bill.
If she doesn't pay the bill, a bill reminder will be sent, no bill payment then power will be cut off.
If you are separating, then get billing put into her name or cancel the account and power will be cut off.