Is the method used to return stolen money to the family, which involved deceiving them by claiming it was a debt or a vow to be spent on a charitable project in their name, considered valid and does it absolve one of responsibility, given that the thief did not intend to steal at the time due to ignorance of the ruling?

You have done well by repenting from this sin. It is not permissible for a child to take money from their parents except with their full consent, unless they withhold the obligatory maintenance prescribed by Islamic law, in which case the child may take the equivalent amount in a reasonable manner. What you mentioned about offering the amount to them as a gift or donating it on their behalf clears your conscience. You are not required to inform them that you took the money from their possession without their knowledge, as what matters is the delivery of the right to its rightful owner. You have offered the right to its owner, and he has permitted you to give it as charity on his behalf, thereby clearing your conscience. We also draw your attention to the fact that some credit cards are permissible to use, while others are forbidden. If the credit card your parents have is of the forbidden type, you should advise them with wisdom and good counsel.