where do you enter child income as an expense on Home and Business

What do you mean by "child income?"   What child income?  Did you pay a child to work for you?

Did you pay your child to work in your business?

If you did, 

1. Go to Business and Expenses
2. Click Edit next to your line of work.
3. Scroll down to Business Expenses
4. Go to Other Common Business Expenses
5. Go to Contract Labor

If your child is under 18, it is best if you issue him a form W-2, rather than paying him as "contract labor".  Children, under 18, working as employees, in the family business, are exempt from FICA (social security & Medicare tax).  So, you enter the business expense as "Wages". 

If you pay them as contract workers, they will have to pay social security & Medicare tax, in the form of "self employment tax".

Reference: https://www.kiplinger.com/taxes/hiring-your-kids-tax-benefits-and-rules