Dogs take work, lots of work. They also take time, lots of time. As you said, it was a learning experience, and you really don't know how much work it will be until you are there. Smaller breeds or puppies are no less work. You have to look at the dog as being nothing less than a child as far as time, work, household arrangements, the whole thing. They are not self sustaining, every day is training day, they will be there for every household event. I've done dogs & kids, you have to go into it with a well thought out plan, a backup plan, and everyone on the same page. Kids have unexpected things come up, dogs do as well, and somehow they plan them to all happen at the same time. A ton of work, but the paybacks are tremendous.
I've always had the smaller terriers, for a lot of years. They are independent to the point of being bullheaded. Most any hunting or working breed is easier to train. They are small, but take up just as much time, household riggery when when younger, and research trying to figure out the hows & whys of their behavior. Once you realize they are bred to think independently underground while dispatching quarry that is often larger than them, you are starting to get somewhere. Pound for pound you are getting more tough little dog than you would with a larger one. I had a Cairn that was seconds away from having my mom's Great Pyrenees by the throat, a stupid situation involving my brother & one of his girlfriends, my dog didn't know my mom's dog was in the house, and happened across her. They don't realize their size, and really don't care, be aware of this if you think a smaller breed will be easy.
Yes, my mom, who was 65 at the time, with a great pyr, second owner. This dog took some work. The Siberian Huskey she got as a rescue when she was 74 took a lot more work, same jumping, food stealing and such you described. How does an older woman, with osteo, a bad back and bum ankle make this work? Many years of previous experience, she knows a lot of tricks.
You didn't come away from this empty handed; you gained knowledge. You are at a good starting point. If you look at this forum in that light, many members come here, not knowing a whole lot about how to properly keep fish. They often make mistakes, but learn from them. The people who learn, and use what they have learned to their advantage have success. Use what you have learned from this and you will have success as well if you are thinking about a dog in the future.
Continue with this learning process. This can and should include your entire family. I can think of no better family outing than going to a dog show. I go every year, along with my wife, friends, and kids who are now in their 20's, to the yearly AKC show in Chicago. This is learning along with a lot of fun. Don't tell the kids about the learning part. Talk to people, learn about the many facets of dog ownership, they are just as varied as aquatics.
My two Aussie Terriers are 2 1/2 & 1 1/2, my first internet dogs. I say this because we did about 3 years of research on breeds, breeders, dog training, all of this as my Cairn got older. So much of this was via the internet, there is such a wealth of information out there now. This wasn't available when I got my Cairn, or the Westie & Yorkie before him. I was lucky enough to have plenty of relatives who were into dogs, besides my mom, as well as growing up around this. Several of my uncles were into terriers, I guess that part may be genetic. I got a lot of info from them before anything close to home computers were common.
There is much more than what they ever told me available online now, and some very good explanations of why what they did, and I learned to do works. Access to gear for the dog, training information, reviews and analysis of the various foods available, what is now just a click away is amazing. Spend some time doing research & planning, the same as you probably did for your first child, as it will be just as new an experience. You mentioned 3 kids, and not hurting the oldest, so guessing there is about 3-4 kids. I'll bet you knew a bit more what to expect with the second kid, thanks to experience from the first. The third kid even more so. I'll bet you also know parents who skimped on this planning & research. It really isn't a lot different with dogs.