Is the mother-in-law's statement: "If my son's wife comes to the house, I will invite the household to a specific meal," considered a vow, and is it permissible for us, as the invited, to eat from this food?

A vow (nadhr) is when a legally responsible person obligates themselves to Allah Almighty to do something that is not originally obligatory upon them by Islamic law. It is fulfilled by any phrasing that indicates commitment. The wording mentioned in the question is not considered a vow unless the speaker intended it as such, in which case it becomes a vow by intention. However, if she did not intend it as a vow, then it is considered a promise, which is commendable to fulfill. The majority of scholars hold that she is not sinful for not fulfilling it, but abandoning it is strongly disliked, due to Allah Almighty's saying: "O you who have believed, why do you say what you do not do? Great is hatred in the sight of Allah that you say what you do not do." [Surat As-Saff: 2-3] And Allah praised Ismail (peace be upon him) for being truthful in his promise, and the Prophet (peace and blessings be upon him) condemned breaking promises and considered it one of the traits of hypocrisy. There is no harm in you eating from it, because even if it were a vow, your uncle's wife made it for the people of the house, which is you.