H.B.
First of all let me say, I know how hard it is to have three young children in the house, mine are 6, 3, and 21 mo. Things can get hectic and loud and not everyone always gets along (we nicknamed my youngest "The terrorizer") But I to share what I have observed when I worked as a Private pre-school Pre-K teacher for 2 years (4-5 yr olds). I also worked in a daycare for 4 years in the toddler room (walking to potty trained) and in the pre-school room for 2 years. And I can tell you that it was agreed between myself and the other teachers that the spanked children were the worst behaved and the least happy, they were the ones typically out of control and whiney, and stubborn, and more likely to disobey a direction. Of course children who are not spanked showed these traits occasionally as well, but the ones who were spanked showed this a LOT more. I am not trying to tell you how to raise your children, I am merely sharing what I observed.
With my own 6 and 3 year old I have discovered that the times when they mis-behave the most is when they are bored or not given any direction (this happens most on rainy days when they can't be outside)so I give them chores. They can empty the dishwasher (not all of it but they do the silverware and plastic dishes) they do laundry (putting my piles in the washer, moving wet to the dryer, and putting dry in the basket, all under supervision of course) they also put their folded clothes in their drawers. I can't even tell you how much this saves me time and energy as well. They also feed and water our cat, and water my plants. There are many other things I ask them to do here and there. It keeps them occupied and they are so proud that they can do "grown-up work."
As far as the separation anxiety, I hate to say I have no advice. I had to quit my gym membership because I was called down to the daycare every 10 minutes because my daughter was screaming. I think that one day they discover that the umbilical cord is gone and they take a while getting over it! But my mantra was "This too shall pass" eventually they get over it, and they are more than happy to let you go so they can get down to the business of playing. There are two things to remember when leaving a child who is upset that will make separation anxiety pass more quickly 1. DO NOT DRAG IT OUT. Say goodbye, give a kiss, and leave. Dragging it out makes it soooooo much worse. DO NOT TRY TO SNEAK OUT. It doesn't work, at some point they realize you're gone and they still freak out but instead of seeing you leave and come back they think you just disappeared. It can be very unsettling for them. Again, say goodbye, give a kiss, and leave. Be as calm as possible because if you are anxious she will pick up on that.
As far as the 6 year old bonus daughter, A lot of 6 year olds test boundaries (I know mine does) they get sneaky, they try lying, and many other things that make you want to pull out your hair. I think just make sure you always hold them accountable, and remind her that nobody likes a liar (it's true, nobody does) and if she doesn't want to be a liar she has to tell the truth. I would also be sure not to jump the gun on issuing a punishment until you get both sides of the story first. Another thing that might help, try playing some team games, kickball and baseball are great, and put them on the same team against you and your husband or against just one of you (we love ganging up on Daddy). Perhaps if they learn to play together as a team and work together that camaraderie will cross over into other times, just a thought.
I hope every thing calms down for you a little (it never completely calms down) before the new little one arrives! Good luck and God Bless!