Kids always come first. IMO
Having raised 4 children I can tell you this -the first one you fuss over, and WAY over protect, the second one not so much -you become more secure in your ability to protect them, by the 3 & 4 -your more laid back cause ya have a good understanding of what's gonna happen.
I did always worry over even non aggressive dogs, and ecspecially puppies. It does not take a heck of a lot to change the course of a child's life by getting a scratched cornea, or facial scars. Until your pup learns to keep four on the floor, and no longer nipping for attention -your sister is right. No use in arguing with a mother. IF
You're looking at it from an aggressive attack situation -it does not need to be aggressive.
Another thing -you can get another dog, but you only get 1 of that little person, as a member of their family you should be doing everything you can to make their time with you awesome!
Play with your dog later, he'll wait
There are lots of great dogs, this world needs more great people