Seriously Alli, yes that is very bad. That dog needs to be bottom of the heap in your family and to know this, right now. You don't want a heartbreaking situation with the children, so sort it out now, this minute.
I think she should always be on the floor, never upstairs and her bed should be somewhere she can't sneak up onto the furniture when you aren't there. The kitchen if there's nowhere else.
I never, ever hit our dogs but if I have to make a point and this is only when they
know they have been disobedient - which is never after they have got through puppyhood, I will give them a good shake and shout.....very loud and a lot. And yes, you can grab a Lab by the scruff of her neck, lift her off the floor a little and shake and yell. Don't let the children do this though.
As with children, no nagging, the fewer rules the better, but those that are there are utterly non negotiable.
If I was you I would explain this to OH now tonight, decide what the rules are and stick to them. Ours are - dogs downstairs, never on the furniture, no toys left with the dog (they are yours, and you allow her to play with them, with you and then take them away afterwards. The reason for this is that they will guard their toys and place they want to sleep.)
Always feed her alone, (outside is good) away from anyone, so you put it down and go away and never do the stupid thing that people try, which is to take her food away from her. (Oh and make her sit and wait for it until you say she can have her meal.) And her bed should be a place where no one touches her or bothers her, this is a rule for the children. Ours had to ignore the dogs if they had gone to bed. No titbits either, there's nothing worse than a slobbering Labrador watching every bit you put on your mouth. Incidentally, you should eat you own meals just before you give the dog hers. (It's reinforcing you as leader of the pack.)
Alli, I'm sorry to be so direct and I don't want to worry you, but this really must be sorted out straight away. If you do this you will end up with a loving family pet who will be a happy dog and always want to be with you. We have no fences at home round the garden, our dogs could go anywhere but they are always much more anxious not to lose us than we are them. I'm looking round now just to prove this and..........and my dog is lying in the kitchen doorway watching me type this. You will almost always be able to trust her (sorry it's usually true,) but we've only had one dog who I would have put money on would never ever bite under any circumstances. And protect her a bit from the children with some peace and quiet especially while she's such a novelty. So ignore those cute melting eyes and make a happy dog who knows her place at the bottom. Odd but it's absolutely true. Trust me. xxxx
PS Those little cat biscuits are ideal for training, as a reward - just one at a time though, you don't want a dog who needs CD! The children can teach her to sit, stay, lie down, roll over etc. using these treats, it'll help her to know her place.
Right I'll stop being so bossy and go now! Good luck, she'll be great and in a little while you'll wonder how you ever felt compete without her. xxx