With small children, I would NOT get a tiny... just me though. That is not saying anything about your 1 & 3 year old, but accidents do happen. When we brought Bunny home and she was 1lb 5oz all I could think was "Grow! Grow!" bc I am so used to have Tino at 4lbs and the worry with such a teeny little thing was HUGE, even in my house and its just two adults to worry about being careful. It just sounds like it would be sooo stressful to have to worry all of the time! I am not trying to be judgemental and tell you what to do, I hope you don't take it that way, I would just wait until your two legged babies are bigger before you get a tiny 4 legged baby!
Does your breeder know that your children are so young?