Having not been there it is difficult to judge any single person who contributed to the situation escalating to the point where security was required. As we now know, the airline in question was Turkish so their rules/guidelines may well be different, which would obviously reflect how the situation was handled.
CAA regulated Cabin crew face this problem on a daily basis and whilst at times it can be torturous and extremely time consuming to rectify, the seating of young children with their adult guardian always gets resolved without the need for security or a stand off. Generally the length of flight determines the level of resistance some passengers offer the cabin crew as to whether or nor they will move seats to accommodate a family. The experience of the crew knowing when to move on to someone else and effectively move to plan 'B' is what generally counts.
Of course making a slot can also determine how wide spread the 'problem' becomes. Usually all efforts to resolve the issue with immediate persons affected or those close by are best. I have at times, had to make a PA to the whole a/c or cabin on wide bodies and explain the situation and request help.
In my mind and certainly if this situation was on a CAA regulated a/c, the calling of security would have been, to a degree, due to a failure of the cabin crew in handling the incident. Of course there are always exceptions to that and sometimes no one can control an incident.
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