You'll need to just make sure that when you file your taxes you add your income in. Your husbands paying in during the year should actually be enough.
If you're not married then this income should not effect you. Most single non working people get tax credits and extra refunds on their own kids and stuff.
If you are in neither of these categories then you need to call the IRS and ask them.
All parents are supposed to get the benefit of claiming any money they pay for babysitting and even if a babysitter does not know they do this it doesn't really effect them a lot. In your case they may ask you for your ss# to put on the tax forms. Then it will go back to you.
I do not call each babysitter I have used over the year when it comes time to fill in the blanks for taxes. I estimate it. Unless it is regular full time care. Then I make sure to include the SS# of the primary care giver.
If I were you and expected to pay in income tax on regular income coming into the home then I would put at least 10% in savings to cover taxes.
If you want to do this more effectively then get a tax ID # and open a small business account at the bank. ONLY, seriously, ONLY deposit the money from babysitting. Then each quarter the bank will help you send in taxes on the money that went through the account. So if you put $50 from a garage sale or a refund from taking a dress back you will be paying income taxes on that deposit. Only money from babysitting goes in it.
Each item you buy from this account that is to go towards the business of babysitting needs to be accounted for too. Food, cleaning supplies, phone costs, a portion of your house payment, utilities, and repairs will be allowed too, there are all kinds of rewards for actually doing this like a business. The federal tax ID will also allow you to get more discounts on your supplies too. You can only benefit from doing this like an actual business.
This way they have a clear set of totals to see. Money coming in and the money you spent on the business. The percentages you will get a discount on will vary from item to item. I got a lot of my phone bill written off due to not using it for much of anything except the EBT machine.
At the very least it will benefit you to make an appointment with a CPA or someone like H R Block to discuss how much you might have to hold back in savings but I expect you won't have to pay anything extra.
If the income puts your household income in the next tax bracket up you may want to let brother take little one to someone else. In Oklahoma a baby would only pay $14.50 up to $25 per day. Our child care is pretty close to yours, you do have a bit higher pay than us but I bet they could find someone else for close to the same if they looked into licensed child care. I can't imagine Kansas being much higher than Oklahoma.