Can my mother combine her vows (slaughtering a goat for the birth of her two sons, and slaughtering a third for acquiring land) into the slaughter of a single calf? And is this vow valid?

Undertaking a vow is discouraged (makrooh). The vow made by the mother is a contingent vow that must be fulfilled if the condition it is contingent upon is met. If her wish is granted (the success of her children and the acquisition of the land), she must fulfill her vow by sacrificing three sheep, as long as she is able. It is not permissible for her to change her mind and sacrifice a calf instead.