Is a single parent travelling with kid entitle to claim family credit for staycation tax credit?

Yes, as per this government of Ontario link below, a single parent with a child is entitled to claim the Ontario staycation tax credit. 

Who is eligible

You are eligible to claim the credit if you are an Ontario resident on December 31, 2022.

Only one individual per family can claim the credit for the year. Your claim can include the eligible expenses of your spouse or common-law partner and your eligible children. An eligible child is not entitled to claim the credit.

If you do not have a spouse or common-law partner, or eligible child, you can claim your own eligible expenses for the credit.

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