From the other reviews and some comments on here from people who have been, it sounds like you had a lucky escape.
And I don't know why you are getting accused of lying here.
Lots of people don't like children in restaurants, well behaved or not. There are plenty of posts on MN by people who choose to go to child-free places or who eat out later in the day to try and avoid them.
There are plenty of people who would complain about being seated near children, or having children seated near them, regardless of how well behaved they were being.
The waitress could have been inexperienced and not known the policy of not seating five people at a table for four, or thought the baby wouldn't count as it was in a highchair, or thought it didn't matter as the two other children were seated on a bench with their mother and so could all fit.
And although on a normal day you might have thought to question why you were being asked to leave, if you were all hungry and wanted to get the children fed, plus if you were feeling embarrassed and wanting to get away before everyone started to stare, and felt that you didn't want to give somewhere so crap your money now anyway, then why not just leave and do as the OP has done, complain later once the children were fed and you'd had time to think about your treatment and decide it just wasn't on?
It's very plausible that all of this happened exactly as the OP has said.
OP some years ago now my mother took me shopping as a birthday treat. We had a lovely lunch and then some more shopping, then at about 3pm decided we could do with a drink and a small snack.
She took me to one of those American diner places that were popular at the time, and it was virtually empty at that point in the afternoon. The bloke seating people asked us what we intended to buy, we said we didn't know until we saw the menu and he said he couldn't let us in unless we told him. My mother said we planned to get a drink and a snack and he said that he felt we wouldn't be spending enough money to justify getting a table and turned us away. They had about three other groups in the place and about 30 empty tables.
We left but my mother was furious with herself later because she just left without complaining.
Sometimes it is a bit of a shock and an embarrassment at the time and you do just want to leave. It's only later that you think you should have stayed to argue or complain.