Firstly I can imagine the security guard was getting overzealous and didn't use his common sense. I suspect the father in question probably wasn't the politest either when challenged. Add the two together and the police were called. Fair enough.
What has clearly gone wrong here is the police response. Sort it out by all means but threatening to use anti-terror laws where there are no reasonable suspicion of the father being a possible terrorist is an abuse of power.
The very draconian laws were given to the police to fight terrorism so should be used sparingly. Misusing them betrays the very trust the police need in order to keep the peace.
If the police abuse their powers then we are hardly going to be willing to give them more, the next time they say they need them. Just like RIPA, that was a law also designed for terrorists, not spying on parents who are suspected of blagging a school place outside their catchment area.
The common sense solution here would have been for the police to look at the photo, no staff/other shoppers, only his own daughter. No crime has been committed. Security have asked you to leave because it's their policy and you broke their (stupid) rules, the exit is that way sir. Have a nice life.