Ninni, I am not trying to offend you by asking questions or telling you things that you know, but you asked for advice.
Actually, I have learned that you can't ever take it as read that people will ensure that their children behave "suitably" with a pup or dog. I don't know you, and you did say that you (and presumably your kids) had not had a dog before. To pups, children (especially youngsters) can be scary, noisy, unpredictable, intimidating, exciting etc - they move fast, have toys and food in their hands and are generally highly stimulating to a pup (or, a bit overwhelming to a quieter pup). It is natural for kids to run up to dogs, run around them with arms flailing and squealing etc. I have experienced it many times with Coco - she is a very (sometimes excessively) confident dog and was the same as a pup - the result was her getting over excited and very bitey with kids which was often not appreciated.
A quieter pup might find it a bit intimidating at first - at least until she is settled and used to it.
Give her space, plenty of rest time and GENTLE and calm interaction and play. Let her come out of her shell in her own time and I am sure she will become more confident in time. I am just asking for advice exactly HOW to do that. I don't want to push her and I figured if there are ways of doing this "the right way".
By gentle interaction and play, I mean never being confrontational with her eg don't run up to her, approach her gently and not face on, maybe approach her with your side to her. Sit near her and play with a toy and let her come to you to investigate. No grabbing or pulling her around (obviously) but just try to lure her into engaging with a fun toy or game.
Having a pup is a learning experience. I was a first time dog owner 10 years ago and like many things you have planned for, it does not usually go quite the way you thought.
I know what it is like to worry about every stage and to feel so responsible for doing everything right for your pup. Far from being the joyful, fun and delightful experience I had imagined, it was actually quite worrying and stressful. During those first few weeks I frequently questioned whether I had made a terrible mistake. I think doubts are very common in the early days. However, I did find that once I relaxed a bit, things were easier for both of us and it did all fall into place eventually.
Sounds like your pup is fine, she is just finding her feet and so are you all. It is a question of her adapting to you and vice versa. In time you will find a system that works for all of you and then you will really start to enjoy being a dog owner.
