I don’t have children, although I think little ones are wonderful, and I think the couple were extremely rude and it really sounds like you were doing your best.
That being said, I have had coffees and meals out ruined by inconsiderate parents and have felt like saying something or asking to be moved in the past.
A lot of parents these days don’t seem to use their common sense or take other diners into consideration.
Example A, I had family, with children, staying at my home during the school holidays when I was supposed to be working from home doing some paid writing work. It required a lot of brain work and research so I decided to take myself and my laptop to the local Costa which is quiet and has sockets for the laptop etc so I could get a couple of hours work in undisturbed.
It was all going well, in fact I was the only person there, when a woman walked in with her 2/5 to 3 year old who was already screaming and charging around like a banshee and loudly announced, “Ok, go on you can choose where to sit!” He looked at me, and presumably my shiny computer, and asked if he could sit anywhere and she said yes. Despite there being another 18 or so tables, of course he chose to sit right next to me. And she left him there unsupervised while she waited for the food and coffees. He went on to climb all over the chairs and tables, talking to himself loudly and encroaching on my table an paperwork. When she arrived he continued to be really badly behaved and she continued to performance parent very loudly and seemed annoyed that I wasn’t up for engaging in conversation and didn’t ask him to sit at their own table when he kept shuffling along onto my seat to look at what I was doing on the computer. I had to stop working until they left.
I would have moved but it would have been a huge faff with all the stuff I had with me. Clearly she had neither common sense nor parenting skills and was used to not having any rules or boundaries with her child.
Example B, I went out for a nice meal with my elderly parents. Again, the kind of set up where you can choose your own table. We wanted a bit of quality time and a nice chat so chose an alcove area where no one else was sitting, sort of like a private dining area.
Not long after our drinks arrived a huge family showed up. Grandparents, two sets of parents and 5 kids under the age of 8. Despite it being a massive restaurant with loads of free tables, they made their way over, pushed three tables together and sat directly behind us.
It was utter chaos. One set of parents had three kids two of which were horrifically behaved. Screaming, winding each other up, throwing things, high pitched shrieking because they didn’t want to eat or sit at a table and because they wanted the baby’s toy or to sit next to Nanna, and now Auntie Claire and so on and so on. These were the some of the older children, aged about 5 and 6. To make things worse, they had one tablet and two phones with a different programme on at full volume spread throughout the tables. One of the couples were constantly shouting at their kids and each other for being unable to cope with their kids and, frequently saying “Ben stop it, you are annoying the people on the other table”, “Freddie, no one wants to hear you moaning, those people are getting fed up with you now.”
Not one of the six adults there showed enough common sense to either move tables, apologise for the behaviour or...not to have chosen to sit with one group of adults sitting alone in a nice quiet area in the first place!
So whilst the OP wasn’t in the wrong, I think that some parents do definitely get it wrong and need to show a bit more consideration for the other people they are sharing a space with.
One of our local restaurants has a separate family area were they sit all the people with children together and all the adult only parties in a separate area. That seems to be one of the better options. The kids area has an indoor play area and a craft table too. Obviously not an option for a local independent cafe but well thought out by the owners of this particular place.