Is it obligatory to obey a mother who prevents her financially independent daughter from performing supererogatory good deeds, such as going for recreation and buying toys for an orphaned girl, and even interferes with the amount of charity given? And would the daughter be sinful if she disobeys her mother in this matter?

The one who sponsors an orphan is he who takes care of their affairs, including expenses, clothing, discipline, and upbringing. As long as you are spending on her from your own private money, your mother has no right to prevent you from doing so. You are not obliged to inform her about what you spend, and you can conceal the matter from her. You must be kind to your mother and treat her well. It is not permissible to abuse her or raise your voice at her, because the right of a mother is great, and honoring her is among the most obligatory duties and the best acts of drawing near [to Allah].