The situation with regards to retail officers and indeed any security officer is that they possess no more powers above a private person (you and I for example)
Under the Criminal Law Act 1997 any person (that's you, me or a security officer) can arrest any person who commits an 'arrestable offence'. Theft (shoplifting) is an arrestable offence. Once a person is arrested they must be handed over to a member of the Garda as soon as practicable.
Thats the legislation.
Now a private person has no right at all to search another under any circumstance unless that person gives his/her consent. This would apply in the scenario you describe (I presume the officer asked the lady for her consent to search her/look in her bag).
Now obviously there isnt enough facts, it might be possible the lady in question is a known 'lifter' and she was observed concealing items by the security officer and he/she arrested her outside the shop and asked her permission to search her bag? I dont know enough to comment but essentially a security officer is on dodgy ground if he/she stops a person outside a shop and that person in fact has no stolen property on them. False imprisonment, defamation, assault springs to mind.
O and to answer your other Q re the tagging alarm going off, no you are not obliged to stop if you dont want to.