I had a dog growing up (my dad hated cats; of course my sibs and I all grew up and each had 2 cats a piece and no dogs). My husband never had a pet growing up. My cats were older by the time my kids were old enough to really notice them and at that age, the cats had very little use for the kids. When we moved 18 mos. ago to a new house with a fenced yard in a neighborhood where seemingly everyone has a dog, the kids started asking. I went to a local shelter a couple times about a year ago, but didn't really connect. Based on breed characteristics and the age/activity of the kids we were looking for mixes with some part retriever or bully breed. A few months ago we started to revisit the topic. My husband wasn't super on-board but he didn't feel so strongly that he was going to say an absolute no. He really didn't know what a dog involved so he felt like he couldn't really totally object.
I must have spent a million hours looking at shelter/rescue websites at the available dogs. I went to visit a few of the dogs I had seen online at my preferred shelter. The next day we all went as a family and we ended up coming home with a 1 year-old (approx.) black lab mix. We looked at 5 dogs that day and spent time walking and playing with each one to get a sense of personality. We saw a lot of sweet dogs, but our kids loved that our dog would fetch (funny what was so important to them). He's a great dog. He's not perfect, but he's learning quickly what is okay and what isn't. The trust is building and he is growing more comfortable with his home/family. I suspect that he may have had some abuse in his history based on how skittish he initially was when we would reach out near his face for any reason and even now I have to take care not to move toward him super-fast with my arm out to grab his collar (like if I want to put his leash on) because he'll cower and it breaks my heart.
He has without a doubt added to the kids' lives, and they all have their own relationships and roles with him. It has also taught them to finally clear their dishes off the table after meals and stop leaving their socks strewn about the house cuz he'll eat/chew on anything he can (lol!)
I will say as a prior cat owner (mine sadly, are long gone and due to known allergies a cat probably is not the right choice for us), you might want to see if your cats are compatible with whatever dog you are considering. The shelter we went with is pretty good about saying if a particular dog should be the only pet in a house, or no small pets, or no kids in the home, etc. I also think that they make you bring in all pets to meet the dog prior to adopting, but maybe it's only dogs that they make you bring...my point is, you want to make sure that the dog and the cats can peacefully coexist before adopting.
Mama to my three:
DD 2/2003
DD 5/2006
DS 3/2010