D.B.
Whatever you're doing is based on what you've heard or read, and not based on her "currency" meaning that which she values.
There is absolutely no study that shows any benefit to spanking - it is used by people who are at their wits end, and it teaches children that pain is okay if inflicted by someone you love (setting them up for all kinds of abusive relationships) or if inflicted by someone bigger (thereby setting them up for bullying, either perpetrating it or receiving it). And, as you've seen, it doesn't work.
Time outs aren't working because they are either too long in duration, too far distant from the offense, or not commensurate with the infraction. Yelling though completely understandable just teaches them to blow their tempers.
It has nothing to do with whether or not you work or stay home - it has to do with your (and her father's) reactions. And maybe the older kids, if they are reacting.
Stop, breathe, think. What does she really value? I'm guessing it's your attention, since she laughs at you. Maybe she LIKES her room, so a time out is not a punishment but a welcome break from the rest of the family and a chance to play independently.
Pick one or two major areas of behavior you want to work on, and ignore the others for now. Is it eating breakfast, getting ready when it's time to leave, cleaning up toys, brushing teeth, wearing a seatbelt, what? Choose two. Pick the two that are not negotiable. If she doesn't do X, she gets one warning. Then she gets the consequence. No arguing, no negotiating, no whining. Deprive her of your attention - do not yell, do not whine, nothing. It gets done NOW or she goes right into "consequence mode". Maybe it's in her room with NO toys - put them in the attic where she cannot see them. If she likes her bike, put it in the garage rafters where she can see it but not get at it. But it has to be immediate. Not brushing teeth today can't result in losing bike privileges tomorrow - too much time between infraction and consequence. But maybe being locked in her room with no one to whine to would really be a huge punishment. Put a gate-hook lock on the upper part of the door if you have to. We let our son keep his special stuffed animals and books, but all the toys went into the attic.
So, she doesn't need to understand why what she's doing is annoying. She just needs to know that every single times she does it, she gets some negative consequence. The main thing is to state your position once or twice, then walk away. Continuing to engage in arguments just fires her up and gives her something to argue about.
Choose a strategy and then STiCK TO IT without constantly switching to a new strategy. Your child will keep testing you until she knows for sure that A results in B, C results in D.
Oh yeah, and put the scissors away. Every kids cuts her hair in some ridiculous cut - it will grow, and the heck with her if she looks ridiculous.
And no it's really really not because you are at home.