Is what was mentioned considered a vow, and what is the ruling on eating from this calf for her and her family, given that she intended to distribute it among friends and family, and did not intend to restrict the distribution to the poor?

A vow (nadhr) is: "A legally competent, free individual obligating himself to Allah Almighty verbally to do something not originally incumbent upon him by Shariah." It is not valid except with a form of words that indicates obligation. The phrase "If the money returns, I will slaughter a calf" does not, in itself, indicate obligation and is not a vow, unless its utterer intended it as a vow, because it is one of the allusive phrases that become valid with intention. If he intended it as a vow, then it is distributed according to the vow-maker's intention. If he intended a specific party, it must be given to that party. Otherwise, it is according to custom. And if not, its destination is that of charity.