A while ago, my parents/brothers and I went to visit a theatre performance (in The Netherlands, where we live). We booked really nice first class tickets with empty seats in front of us. We booked them very last-minute, hoping we would be lucky, and we were. A few of the seats in front of us were still empty during the performance. After the break, what looked like a mother and her daughter (in her early teens) entered the row in front of us, and stopped at the seats in front of me and my dad.

I clearly overheard their talk, and the girl was telling her mother that these were not their seats, that their seats were about 5 rows further back. Her mother tried to keep up the act that these were their seats though. In the end, she noticed they now had our attention, and asked us 'Are these seats taken?'.

Mom and dad were hesitating, so I just cut in:

No, these seats aren't taken. And no, they will not be taken either. We booked our seats this way, so maybe no one would be in front of us. I clearly overheard your daughter telling you that you booked seats about five rows further back, so please go to the seats assigned to you on your ticket, or I will go and fetch an attendant to remind you where they are.

Might be of interest that we booked 1st class tickets, and that about 2 rows further back, 2nd class started. So they were basically trying to get a free upgrade. Also note that taking seats that aren't assigned to you is breaking the theatre's house rules.

Despite my answer, the mother sat down, and pulled the girl into a chair as well, the girl already looked majorly uncomfortable and embarassed at this point. So, I got up, didn't engage the mother further, fetched the nearest attendant like I had promised, and they came with me to remove them to their own seats.

The girl's mother started insulting my mom, telling her she had done a poor job raising me, that the only thing she did right was feeding me (I am overweight, ouch). At this point, only the attendant's presence probably prevented this from escalating into a proper, physical fight. This ladies remarks managed to take away some of the good spirits we were in that evening, despite us all having had a really good time up to that moment, and us trying to dismiss/joke it off afterwards. We were all a bit less cheery for the rest of the evening.

While the attendant escorted mom and her daughter to their proper seats, I started feeling bad for the girl, she was looking so embarrassed with the way her mom was behaving, we were feeling less cheery but she was close to tears.

I get the impression something in my response/actions triggered all of this, but I can't really put a finger on what it was. So, next time someone takes seating not assigned to them, how can I handle the situation in a way that won't make the other person feel a need to be nasty and ruin our cheerfulness, while at the same time prevent possible children of being embarassed by their parent's behavior?

There have been a lot of comments saying it's not 'my job to enforce the rules' or that these people were perfectly entitled to take those seats, so to clarify a bit further to avoid this confusion:

In the Netherlands, it's perfectly acceptable (and even expected) to point out to people that they're breaking a rule and inconveniencing you, before getting any authorities involved. People talking in a silence carriage, people smoking outside of smoking areas, people taking seats that aren't theirs to take, neighbors causing stench by having 30 dogs: It's expected you point out that there's rule they're breaking, that they're inconveniencing you, and only after go fetch an authority.

So yeah, while it's technically not my job to 'enforce' the rules by physically moving these strangers to their proper seats, it's my 'job' (duty?) to tell them, when seeing people trying to take seats that aren't theirs, and being asked whether these seats are free, that these seats may be free but not theirs to take according to the rules of the theater, and to let them know breaking it will get them into trouble.

If they hadn't asked, and I had seen them commit the offense, I could've silently flagged an attendant or pointed out their mistake to them in a more gentle way, like 'Hey, we didn't see you here before the break, did you miss the beginning?'. But by asking whether the seats are free (which, as LordFarquaad pointed out in their answer is equal to confessing you're trying to commit an offense), the burden was up to us to tell them that they were trying to break the rules being fully aware of them (which is slightly worse than unknowingly breaking a rule).

A lot of people might be thinking that I'm only taking offense to the seat being occupied, but the combination of them deliberately breaking the rules in combination with them not paying for the seats and limiting a view, all while engaging us in the process, is what makes it worthwhile enough to be assertive.