yes you do. you have control over where the proceeds go. the amount that goes to charity would be reported on schedule A. it is not a business expense.
Yes, you would have to claim (report) the income from those classes and then claim the amounts as charitable contributions. Charitable contributions are subject to limitations, especially in that you would need to itemize deductions on Schedule A of Form 1040. (There is a limited COVID-19 exception to itemizing for up to $300 of 2020 cash contributions).
If you either received income (by cash, credit card, pay sites, or check) and sent it elsewhere or had control over income (cash, credit card or check) and directed it to be sent elsewhere, it is still your income and reportable on your tax returns. The key elements here are the fact that the income came about as a result of your efforts, and that you had control over the receipt of that income.
EXCEPTION: If you are reporting your yoga income on Schedule C and the specified charities actively promote your yoga teaching business, you could consider the contributions as Advertising" expenses, fully deductible from your Schedule C income. The income would still get reported as "Income" but you'd be deducting the same amounts as "Adverting Expense."