Unless they had of coursed booked the seats and had evidence. I'd be pissed off if I took the time to reserve seats and others that didn't then chose to sit in them. Thing is, did they have any evidence they had reserved them?
Well you lost the high ground as soon as you walked away. Next time, if there is one, just take a photo of her (not her kids) sitting in your seat and just say that you will need it as evidence. She will either move and you get your seat or you write and complain to the rail company saying...