Yes, as a caregiver is just someone who watches a child. So the teenager next door is a caregiver while you are your husband are at the movies.
If you are asking if a step-parent has any legal rights, generally no. However, most places accept the non-parent spouse as acting and authorized by the actual parent spouse and give no true hassle. If someone does give a hassle, a child care power of attorney works to allow the person to take the child to the doctors, sign school papers, and anything else that is put into the document.