You can withdraw or clear from "regular" savings accounts whenever you want for whatever you want. You just have to watch out for interest penalties if you make too many withdrawals in a given period and you may also have to serve a notice period.
The main aim of regular savings accounts is to facilitate regular monthly payments into them by direct debit or other means. There is no real reason to leave large lumps sums in them unless there is a particular reason.
If the interest rate is better in the Rabo account, why not move the money across? Then just keep the regular payments going into the AIB or a new account.
Also, just because the likes of the Rabo account is not designated as a "Regular Savings Account" doesn't mean that you can't regularly save into it e.g. pay a regular monthly amount into it using your online banking. That's what I do with my Rabo account. Interest rate is still decent and you have instant access.