Will My Dog Attack The Babies If She Is Already Attacking The New Puppy ?

This could be very serious. I think the problem is mainly to do with competition from the pup and she's making sure it knows that she's dominant but do you want to take the risk. I would advise getting help from a dog trainer. It doesn't have to be private as I realise that can be expensive but if you join an obedience cl the trainer should address any issues that you have and offer help and advise! I wouldn't risk leaving this to find out what happens, better to have some peace of mind and find out either way.