Santa brought my two girls a puppy last Christmas. Their dad had died in August, so they needed something to love and care for. My girls were older though, 5 and 7 at the time. Santa brought a Soft Coated Wheaten Terrier.
I did alot of research on dogs. I didn't want a big dog because I was renting at the time, but in the same token, I didn't want a small dog either.. too easy for them to get hurt when small children play with them. My wheaten is a girl, and she now stands about 18 inches from her shoulder down, and is about 35 pounds. She is very playful with the girls and with other dogs, when she is alone, she is very gentle and quiet. I never had a problem with her chewing on things, but she is a terrier and she did dig a little when she was younger. (she is now about a year and a half). She doesn't shed, which was a HUGE plus for me, but you will have to have her groomed (I keep her coat short) or you will have to brush her. (This is something fun for the kids to do.) She doesn't BARK... I have heard her a couple of times but for a dog.. I would say she doesn't BARK. She loves other dogs and I have never heard her growl or try to bite anyone. She loves to curl up on the couch with me and the girls.. She is a very intelligent dog, and that is good and bad. :-) Potty training here was not that difficult.. but it took a good 6 to 9 months to get her fully trained.
I did alot of research on different dogs... and this breed just really fit what I was looking for. I had never heard of them before, but now, I am so glad I chose her. She is the perfect compliment to our family, and my daughters and I both just love her to pieces.
Good luck on finding the perfect dog for you... As long as you know you will be the one taking care of her and cleaning up after her, and not your child.. then there shouldn't be a problem. My girls do help with baths and feeding and watering her.. but I am the one responsible for making sure she is watched and fed and let out.
Things you really need to do from the start is crate train her from the very beginning, and keep her on a schedule. With you being a stay at home mom, it won't take you too long at all to get her trained. My dog stays in the laundry room during the day while I am at work, and in her cage at night. She loves her cage and knows when it's time to go to bed, she crawls in without a peep.