Dotsie and Sadie do not write for the Ankh-Morpork Times; they have been around quite a lot longer than journalism(1). The agony referred to is entirely real. The two elderly ladies provided protection for Ladies of Negotiable Affection for decades, before the Seamstresses' Guild and when the City Watch was neither willing nor able. Indeed, after the Watch did recover its strength it didn't need to worry about Seamstresses, so efficient and notorious were the Agony Aunts. The rare individual who might make a complaint after one of their interventions would be told by the Desk Sergeant that he was blessed to be able to do so, and not to press his luck.
The Agony Aunts maintained order in the "entertainment district" on the margin of The Shades by a policy of Eventual Assured Destruction (parodying Mutual assured destruction). They never hurried; they preferred to let a miscreant worry while they sought him out, but vengeance was as inevitable as sunrise. Eventually, their handbag and umbrella would come down like the Assyrian to the fold, and another example was displayed to warn other stiffs and lowlifes against troubling the seamstresses. Dotsie's unnaturally heavy purse was used for quick removal of any threat; Sam Vimes thought she probably outclassed Dr. Lawn in the narrow field of mechanical anaesthesia. Sadie's parrot-headed umbrella was a double-ended instrument of terror which would provide much of the actual agony. The two were elderly more than thirty years ago and have probably retired (or died)(2), but their memory, with the strength of the new Guild and the improved Watch keep order around the Whore Pits still.
It might be that the Agony Aunts are more than they appear, like Bill Door, Ronnie Soak & Wilf they have adapted to a new role. Vimes recognises them 30 years in the past, yet they are still alive and apparently no older in the present time. Also they have a strange ability to hide in the darkness, or emerge from it, that even Vimes didn't spot them. Roundworld Mary Poppins also used a parrot-headed umbrella, and she was more than human. Described with their dark hood-like bonnets, perhaps the Aunts are female ring-wraiths or the forgotten virtues Bissonomy & Tubso standing up for women. But it is nice to think they are just two strict ladies who can put the fear of god into any men who take advantage of the Seamstresses.
(1) For Americans who don't get the joke, "agony aunt" is British for "advice columnist"
(2) They were still active at the time of The Fifth Elephant, however. Perhaps they have acquired a staff (though it probably does not have a knob on the end).