Is the mother's failure to fulfill her vow to sacrifice a ram upon the birth of her daughter the reason for the daughter's delayed marriage and her rejection of suitors, and what should be done if the mother is unable to fulfill the vow?

Your mother must fulfill the vow because it is a vow of obedience. If she is unable to fulfill it currently and does not expect to be able to do so in the future, then she must offer an expiation for a broken oath (kaffarat yamin), which is feeding ten poor persons or clothing them, or emancipating a slave. If she cannot find any of these, then she must fast for three days. It cannot be definitively stated that delaying the fulfillment of the vow is the reason for the delay in your marriage, but it is possible, because sins can be a cause of calamities and deprivation of sustenance. The questioner should not reject anyone who proposes to her if his religion and character are pleasing.