Having seen this sort of thing before, occasionally, I would be pretty sure there was a temporary change to another aircraft type and then it reverted to your booked type, thereby losing your assignments. It's very disappointing when this happens, since you did the right thing by reserving in advance. If you can, I would bring a print of your seat payment, since cabin crew's responses to this tend to be influenced by whether the passenger did pay for seating. Suffice to say your aircraft will not take off with you separated from children that young. Unfortunately I don't think the Engagement Centres can move other passengers around since there may well be other child or disability passengers who can't just sit anywhere. If there are other WTP seats available now, then that is different and deserves a HUACA. Expertflyer will show this, or you can give your flight details here. If it is full it may well be that check-in staff can't do much either, so it will fall to the cabin crew to resolve. Luckily the IFM will probably be quite good at sorting this out swiftly.

After travel I would reclaim your seating costs and also ask for a customer service gesture for the problem this has caused.