A - Thanks for the questions. I know you must be wrestling with such a difficult situation, so I will keep you in my prayers and ask that our readers do the same.
The Catholic Church teaches that our fertility is an beautiful part to our humanity, so to have a woman's tubes tied (technically it is a tubal ligation) or for a man to have a vasectomy, is a mutilation of our bodies for a utilitarian purpose. This is because it requires a surgical procedure that renders a person infertile. It treats our fertility as a bad thing and not the gift that it is. (For more about what the Church teaches about contraception and surgical sterility see the links at the bottom). Just a side note, no tubal ligation or vasectomy can be determined to be 100% effective. There is about a 1% chance that it did not work and a chance of pregnancy still exists. Furthermore, many woman regret their tubal ligation because of health issues, psychological issues, loss of fertility, and guilt.
That being said, many people struggle to follow the Church's teachings. It isn't easy to live a chaste life within marriage, because chastity (the proper ordering of our sexuality) requires self-control and discipline. In many marriages this might mean the sacrifice of periodic abstinence within the marriage. This isn't easy. But, it is worth it.
To directly answer your first question, your wife is under no moral obligation to have her tubal ligation reversed. But, she is under the obligation to confess her sin with true contrition before receiving any other Sacraments, including the Eucharist. If you went along with the surgery, then you too should go to Confession.
The decision to have a tubal ligation reversal should be discerned through prayer, consultation with a good priest, and consideration of the factors in your life (e.g. desire for children, health, risk of surgery, chance of successfully reversing, etc).
Now, if you wanted to "give up sex as a sacrifice" is a much more difficult question. I do not have enough information to answer this question. Is it hypothetically possible? Yes. But, for your situation I would highly suggest you both go talk to a good priest who can help you sort out the reasons you might be considering this option.
I hope this helps.
Additional Links:
*FAQ on Contraception
*Humane Vitae and the Catholic Church.
