I am wondering if there is another dimension to this.
A problem that I can see if the flight had just continued to its destination is that it would have created a public precedent concerning how passengers can behave in relation to flight crew. I.e. that the mother could have demanded something with threats of violence, and then be seen by the other passengers to have gotten her way.
IMHO if such precedents are created, it isn't just a matter of the pilot feeling put out because the crew 'lost' or something, but a general erosion (over time if there are similar incidents) of flight crew authority, which could lead to passengers being more likely to argue the toss with flight crew, and not follow their directions, which would have safety implications.
I don't think it's necessary for this to apply for it to be the correct decision to deplane the family. Just the threat of violence is enough in my eyes. But, I see many comments (e.g. in the Independent newspaper) saying that since the girl had calmed down, there was no need to deplane the family. I've been thinking that the precedent that would be created could have been considered by the pilot.