Could you not have withdrawn funds from the other account which receives your income and where funds were presumably available for you to live on for the 3 weeks that you were overdrawn by this 'small amount'? How much was this 'small amount' by the way?
You can't blame this on contactless. You have only yourself to blame.
I find it strange indeed that the fees charged (Â£90) for the first period are identical to the fees charged for the second period. You say you were in unauthorised overdraft for 3 weeks. So it looks as if this 3 weeks went into two separate charging periods, but that still does not explain why you were charged identical amounts for both periods. Are you sure that this Â£90 has actually been debited twice? Remember that the fees are debited in arrears so the first fee would not have been debited until some time after the account was allegedly (see below) back in credit and the second set of fees one month after that.
You claim that you put the account back in credit but that really cannot be if you are now Â£180 over your overdraft limit. Do you actually mean that you reduced the overdraft to the overdraft limit?
In order for you to now be Â£180 over your overdraft limit you must have returned the balance to -Â£250 (your overdraft limit) exactly then ignored the situation when the first lot of fees were debited and the balance became -Â£340 and paid in not a single penny ignoring the situation for another whole month before the second set of fees hit one month later increasing the overdraft to -Â£430. Be warned that another set of fees will also be debited next month!
Perhaps the best thing for you would be to limit yourself to one bank account (the one which receives your income) when this situation is sorted?
I am actually surprised that RBS continue to offer you an overdraft facility on an account which does not receive your income and that you don't appear to actually be paying any money into each month. I am not at all surprised that they won't refund any fees as a goodwill gesture on an account which is conducted in this manner.
RBS charge Â£6 per day with a maximum charge of Â£90 per charging period.