Each of these issues can be solved but it’s whether you want to put the effort in.
She sounds like a classic understimulated dog which is no surprise considering you are a mum of 3 and your husband works.
Firstly which breed is she and how old?
How often do you walk her? She needs 2 walks every day. Your husband should be doing one of these, either before or after work.
Buy some puzzles feeder- a simple ‘slow feeder’ bowl will work, or kongs or lickimats. Use these for her meals to get her brain working and distract her for a while- especially during your own meal time.
Slow feeders are good- you can pour a bit of weak broth, stock or gravy in the bottom, scatter her dry biscuit on top and freeze to make it last longer.
If she’s pulling on a walk, then try a gentle leader/halti. Walk with her (by the side of the pram if you necessary) and every time she pulls, stop dead. Only start walking again once the lead is loose.
Perhaps think about getting a waist belt so you can walk her hands free if you have the children.
Why is she barking- because she can see/hear external stimuli?- block the stimuli- don’t let her see out the window for example.
Or because she is left out there and wants attention?
Keep her on a lead in the garden, and if she barks, grab the lead and bring her in.
Sitting in bed- why do you want her in the bed? You can teach a ‘settle’ or ‘in your bed’ command by leading her to her bed and giving her a treat. Keep taking her back to her bed and asking her to lie down.
Dogs do follow you around, they want to be near you.
If she’s getting enough exercise she should settle down easier.
Chewing the toys- ideally you would remove anything you don’t want her to chew but that is hard with children. Have a supply or chews and tug toys and replace what ever she is chewing with those. Always replace the toy with something, don’t just take it away.