Edited to remove option of banning the dogs (although, according to the story it seems like the airlines are able to restrict which dogs are allowed?).
How do you suggest we deal with this? A boat would be far too slow, and a private jet would be far too expensive.
In these circumstances, I will bring my toddler in the plane, try to keep him quiet, and bring baggies with complimentary snacks and earplugs for the passengers sitting next to us. I don't think I can realistically do more than that.
What I'm not going to do is wait five years until the child is older, because I have no assurance that my parents will be alive by then. Sorry if that inconveniences you.
It is never necessary to fly with your dog uncaged in the main cabin. Ever. Full stop.
First, a two year old isn't a new born. Having 3 kids, I can tell you that a new born is far less trouble than almost any child up to about 6 years of age because they sleep 16-20 hours a day.
There's nothing wrong with traveling with children as long as the children are well behaved and you plan your flight to coincide with nap times.
My wife and I flew from NY to London next to a family with 3 children all under 6 years of age and they were delightful. The gentleman taking up one of the seats in the row they occupied however was a piece of garbage. He had the aisle seat and when they showed up he let out an audible sigh and made it abundantly clear he was displeased with them. We had an empty seat in our row and were going to offer it to him but by the time they closed the doors he had proven himself to be such a disgusting human being that we chose to keep it for ourselves.
You seem like a decent person trying to minimize the disruption your toddler is causing the other travellers, but in my experience you are definitely in the minority. I can honestly say that I've never met anyone that did what you say you'd do.
The far more common example is parents that pay no attention to their kids, regardless of their little angels kicking the seat in front of them, running and tackling the crew, throwing food or liquids around or just screaming at the top of their lungs. The only moment the parents seem to react is when other travellers ask them to control the beasts, at which point they'll start screaming about strangers telling them how to educate their kids.
Again, you might not be like that (you are probably nothing like that) and we all accept that, even if your toddler is causing discomfort in others, you have no other option. Maybe accept that some of that people travelling with pets might not have any other option either.
By virtue of its universal applicability, your comment says everything and therefore nothing.