Upon the death of the stockholder his interest shall pass to the oldest son or oldest daughter.
I am the oldest daughter and have a younger brother. Who gets the interest?
My suspicion is that you have fallen foul of wordy American drafting by someone who isn't used to dealing with succession issues. This is the stuff of which very expensive family disputes are made.
There's no linguistic suggestion that it definitely privileges one gender over the other. I would suggest that to an English lawyer, the most natural reading would be that it means "eldest child", especially if there is an interpretation clause that provides that one gender imports all others.
The actual effect of this provision may not be to determine devolution of the interest, but to restrict the possible modes of devolution, depending on the type of document this is. In that case, it means that the interest may be left to either the eldest son or the eldest daughter, but to no other (presumably excluding the second daughter who is oldest than the eldest son). That is to say, the interpretation of this sentence very much depends on the other contents of the document, and the type and effect of the document.
I strongly suggest that you, your brother, and parent get together with a lawyer and resolve this before your parent dies, if there's much of value at stake.
My first thought was this is a question about legalese that would probably get closed. My advice to OP is consult a lawyer if the meaning is important to her. My layman's opinion of the text is...
oldest son or oldest daughter implies oldest son if there are any sons, otherwise oldest daughter. So OP's brother will inherit.
In Sweden (and some other royalist countries), there is now the idea of a "fully cognate succession." That is, the oldest child will inherit the throne, whether boy or girl. Depending on the context, it could have a similar meaning here. It's no longer clear whether the oldest SON comes first, if he has an older sister.