I am signing on again merely to respond to this post because the answers given up until know are wrong, in part or totally, and unhelpful to the OP, at least as it relates to marriage and annulment. Canon law of 1983 is now in effect, not 1908, and the old Catholic Encyclopedia is NOT a reliable guide to canon law issues today.
If you are living with the young lady but not having marital relations, no you are not committing adultery. You may be giving scandal to those who know you, which is another issue, but that is the proper concern of only a few people. You must discuss this with the priest who is in charge of your Confirmation preparation and be guided by his advice. Speak to him this week, as he will be very busy Holy Week. You are however setting and example for the child who lives with you and must be guarded in all aspects. You have also established, by virtue of the fact you are functioning as a household, a relationship not only with the young lady, but with her child. That alone is very dangerous and potentially harmful if this relationship does not lead to marriage, for the damage that will be done to the child who has come to trust and possibly love you during this time. Not to mention the natural pain that will come to you and the lady if there is a break-up. Please take this into account whatever you decide.
If the facts about her first marriage are as you relate (and bear in mind you may not be in possession of all the facts) her first marriage is invalid due to lack of form because the Catholic party did not observe the laws of the Catholic Church on marriage. This by the way has no effect whatever on the status of their child. Should she wish to marry you or any Catholic in the future, she must submit those facts to the parish priest who will guide her through the rather simple paperwork process which establishes in writing the fact that she is free to marry. This is NOT an annulment, and Rome is NOT involved, this is handled on the local diocesan level.
The young lady is NOT required to convert in order to marry you or any Catholic, but her freedom to marry must be established. This leads to a deeper issue you do not mention, which is how will children of this new marriage–if it happens–be raised? She needs to make no promise, but you as the Catholic party must promise to welcome children God sends you, to have them baptized and raised as Catholic, to the very best of your ability. You two must discuss this, and perhaps other issues you have not yet considered before you plan to marry, and should have discussed them before moving in together. This would be true no matter what your religion, marital status, previous relationships etc., no matter who you are or who you marry. That is why the Church wisely provides a marriage preparation process, so that couples confront and come to agree on the essential issues surrounding marriage and family.
The old Richard Dreyfuss movie “Goodby Girl” with all its moral ambiguity, does a good job portraying what can happen when a boarder or roomate, male, develops a relationship beyond that with the landlord (female) and moreover, her child, and the damage done when that relationship breaks up, especially the damage to the child. Another good movie that shows how the child suffers through the relationship ups and downs of the parent is “Jerry McGuire”. should be required viewing IMO for any man or woman considering a live-in relationship with a person who has a child.
I raise these issues not to criticize but to direct your thinking in an area that, from your posts, may not be at the top of your mind right now, but which may be very helpful for you to consider during your Confirmation preparation. Remember that the sacrament will incude a profession of faith, and that you must understand enough about Church teaching, on morals and marriage as well as other doctrine, to make that profession sincerely. Perhaps because I deal most directly with the children in such cases, I tend to see things from their perspective.
the proper terminology, to correct some previous answers, is that a Catholic is obliged to marry in accordance with the laws of the Catholic Church, that is, to observe Catholic canon law on marriage. When we say “must marry in the Church” that is rather confusing, as it may be taken to mean, “in the Church building” which is incomplete and inaccurate.