Short answer: Yes, you can change your paystub. Your payroll people can change it for you.
Long answer: The paystub "withholding" is simply your best guess as to how much money you will owe in taxes at the end of the year. You have that amount "withheld" as a means of prepaying your taxes. Rather than saying, "I want $400 withheld because I think I will owe $4800 in taxes," you just withhold based on your status (married with 2 kids, for example). If you guess wrong, you either owe money or get a refund, depending. "Married using single rate" means that even though you are married, you have chosen to withhold as if you were single.
As an example: When I got married, I forgot to update my paystub. So this meant that even though I got married in 2014, for several months I was withholding at the single rate, just like you and your wife. For my wife and I this means I was having WAY too much withheld. She doesn't work, so when we file our taxes, we will get to use the married deduction but there's no additional income, since she doesn't make any money, so we will get a big refund.
Many people on this forum purposefully manipulate their paystub withholding for various reasons, just as you are imagining doing. For example, a single person with rental property operating at a loss (say, -$10,000) would have a an "adjusted gross income" for tax purposes that is $10K lower than their actual salary. That means that if that person wanted to get their refund to $0, they could change their paystub to withhold less money. How do you do this? By saying you are "married" instead of single. Or, if married, you might reduce the withholding by claiming an additional exemption for a dependent you don't actually have.
It can be a tricky game, because the IRS doesn't trust people to just pay all of your taxes at the end of the year, and they will actually penalize you if you estimate wrong and end up owing too much. So you wouldn't want to change your withholding to "married with 10 kids" and then pay all of the taxes at the end of the year. The goal really is to get as close to "0" as possible.
In your case, it seems like you may have done the "right" thing by withholding at a higher rate by accident, since your wife will have additional income from her LLC for which no estimated taxes were paid throughout the year (I'm guessing). I don't know the rules off the top of my head, but usually businesses are required to pay estimated taxes quarterly, in the form of just writing a check to the IRS. This equates to withholding from a paystub when you work for someone. Again, if you don't do this and end up owing too much money at the end of the year, you are penalized. It's possible that your accidental extra withholding will balance this out.
One other thing - my employer (and I'm guessing most) adjusts my withholding to account for my 401K contribution. So when I get a paycheck, the amount of withholding isn't based on my gross, it's based on my gross minus the amount I put in the 401K. For example, if my gross is 6K, and 1K of that goes into my 401K, my employer only withholds based on 5K. So your math might be wrong.
I know most folks around here are EXTREMELY adverse to paying for financial advice. But in your case it may make sense to go to a fee only financial advisor to discuss your tax situation. You don't seem to be super-educated about how taxes work, and filing taxes with an LLC can get pretty complicated - is this the first year you've done it?... You CAN do it (it's not that hard) but you have to educate yourself, either by talking to someone or reading up. You don't want to end up paying penalties because she was required to pay estimated taxes and didn't. If you want to try to educate yourself, go to irs.gov, click "forms and publications" and start reading publications that align with your situation. If you've never filed taxes for her business, I would start with that one.
Good luck!! For full disclosure, I am not a CPA. I'm a Navy JAG (lawyer) and ran the free tax center for military members several years ago. I made myself smart enough to do that by reading tax publications. If I can do it, you can, too!!