What is the effect of having joint (JTWROS) accounts with mom on $13,000 gifting and look back rule?

1) Medicaid will consider ALL of the money to be your mother's, since (a) the money was all from your mother in the first place, and (b) she has the right to withdraw any or all of the money as a joint owner. Therefore, all of the money in the account will be considered an asset of your mother's in determining eligibility.
2) I'm not sure about your question on gifts. Are you asking if your mother can use some of the money from this account to give you a gift? If so, the answer is yes.
3) About your question if you can use some of the money in this account to give gifts to your husband and son, the answer is yes. As I indicated above, the money in a joint account is available to all of the joint account holders. Your mother might not like your giving this money to your husband or son, though. If you do give the money to your husband or son, Medicaid will consider it a gift from your mother to you and use the five-year look back rule to bring it back into her assets for determining the penalty period.