How can my mother get a B2 visa to attend my daughter's first birthday if her visa was denied before?

You will need to address the reason for the denial in the first application and demonstrate sufficient ties to the home country so as to make her want to return. This can be employment, ownership of property, apartment lease, bank accounts, etc. You can also purchase round trip tickets in advance (refundable fares are advised). You should also write an invitation letter where you guarantee her support in the U.S. and her return to India.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. Why was her prior visa application denied? Does she have proof of non-immigrant intent? I suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your mother's situation. (S)he would then be in a better position to analyze her case, and advise you of your options.

It is do-able. It is highly recommended to work with an attorney due to the past denial, who will prepare a good case in your behalf. There may be other options too if you are a U.S. citizen.

Your case is not so unusual, and based on the information you provided, this is how the consular officer sees this case. B-2 applicant is mother of a U.S. citizen, who just had a baby. U.S. citizen and his spouse need baby sitter. Mother is likely coming to take care of couple's baby and is unlikely to return to India after brief stay in U.S. and U.S. citizen son in most likelihood will file petition for mother once she arrives in U.S. A B-2 visa will not issue unless you can convince the consular officer otherwise.