I've scan-read the thread, so might have missed it, but I'm confused by all the people saying feed the baby off your plate. It makes no difference whatsoever to the restaurant's takings whether you feed a baby off your plate or bring your own food. Either way, you are not buying the baby a meal, so it's a stupid argument.
Next time, OP, instead of getting yourself in such a state that you are "fuming", just quietly ask to speak to the manager/supervisor/shift leader, and ask if it is a policy, or if the waiting staff are just being a little over zealous.
I spent my entire 25 year career in the hospitality industry, and it does make me chuckle, the preconceptions a lot of people have about restaurants.
I would imagine, in your case OP, that at some point the waiter had been told to tell someone that they couldn't eat their entire picnic in the restaurant. He then probably thought "oh look , someone eating their own food, I'd best sort it before the boss sees".
Most restaurant managers want and need customers. They also want and need those customers to A: come back and B: write nice things on Tripadvisor. Believe me, no restaurant manager with half a brain would risk a bad review online for the sake of a pot of pasta.