Yes, a married woman can convert to the faith alone. Her husband is not required to convert or sign anything agreeing to raise children Catholic. Since this woman and her husband presumably entered marriage to each other planning to raise the children non-Catholic, the woman should respect that and not insist on the children’s conversion. What she can do is to pray and offer up her sufferings for her family’s conversion. She can also let her husband know that if he wants the children educated in the religious tradition they once shared and to which he still holds, it will be primarily his responsibility to form the children in that religion and to make certain they meet their religious obligations.
If the non-Catholic husband expects his Catholic wife to take primary responsibility for the children’s religious formation, then he has no grounds on which to deny her the right to teach the children according to her newfound Catholic convictions. This also holds true if the husband is uninterested in forming the children in any religious tradition. The wife has the right to ask that the children be given religious training and opportunity to worship God; if that is not done, she has the right to do it herself according to her own beliefs.
