It depends on how much you baby your bags and what you are okay with.
I do have the denim in a size small and I am a person not to baby my leather bags. I have a few leather bags that if my friend's babies or family member's kids (ranging from 2-6 years old) were to throw them on the ground or pour juice on them, it would not make me upset.
But denim is fabric, and that's a bit of a different story.
The denim material itself is not that prone to scratches, it can probably take a few bumps here and there and the flexibility of the bag means one does not need to worry about warping in structure. It is a comfortable bag to wear and can definitely store a lot.
However because denim is cotton it can stain and absorb liquids, oils, and odors. The shoulder strap is also suede, which can stain as well. I refrain from taking this bag out to restaurants that have a lot of smelly foods, steam, or smoke. (Also don't take it out when it rains, but that's probably a given lol)
I do not have any children, but I have a 2 year old crazy (but adorable) dog, who sheds like crazy, loves to jump on me when he gets excited (dog nails) and likes to lick a lot of things (plus sneeze). When I bring him out, I bring a tote made of coated canvas. Have not worn my YSL denim puffer bag with him out and am not sure if I will do so until he grows up a bit more and calms down.
I'm not saying this is not a great bag for your purposes, like carrying baby items, your necessities, etc. Just some food for thought.
Hope that helps!