Dear PW,
Speaking from my heart to you. Please try and not beat yourself up, thinking you will not be a worthy wife for a traditional Catholic man, or that a traditional man would not want you for his beloved wife. IF a man has that attitude, then shake the dust from your feet.
As Catholics, when we confess our sins humbly, sincerely, and in repentance with the firm purpose of amendment, and the priest administers absolution and gives us our penance, that sin is FORGIVEN! You are not to wear a scarlet letter, or the like. Remember, through the sacrament of confession, our souls are made as PURE and clean as the day we were baptised! What a gift and grace from Our Most loving and forgiving God! Yes, God is also just, but His justice is tempered with Mercy. This idea that you are to be cast out to the nether world and undeserving of a joy-filled life to share with a Catholic husband, is nonsense!
You might just be surprised at how many trad Catholic men would find you to be a suitable wife. I think it would be an act of humility and mercy to take a wife with a child; I think it would be heroic and virtuous for a man to do so. First of all, a marriage first and foremost is ordered toward sacrifice. It would perhaps be a very big sacrifice for a man to marry you under the circuмstance. Our Good and Gracious God will surely reward such a SELFLESS act!
You say you "might actually have a few positive things you could bring to a relationship". Do not sell yourself short! From the little I can gather, I'd say you have many good qualities.
Do not let anyone's post here "make you question a little bit whether or not your efforts to prove yourself will be fruitless". Leave your efforts in God's very capable Hands! Trust that if it's in His holy will, He will indeed send you a good Catholic man to be your husband. I know a little something of what I am speaking about here from personal experience. Take heart and have faith, trust, and courage!
Remember this PW:
What man of you that hath an hundred sheep: and if he shall lose one of them, doth he not leave the ninety-nine in the desert, and go after that which was lost, until he find it? And when he hath found it, lay it upon his shoulders, rejoicing: And coming home, call together his friends and neighbours, saying to them: Rejoice with me, because I have found my sheep that was lost? I say to you, that even so there shall be joy in heaven upon one sinner that doth penance, more than upon ninety-nine just who need not penance.
Our Lord Jesus is the great Physician who heals our souls from our infirmities. He came to heal the sick, the sinner, for the well are not in need of the Divine Physician!
Stay focused, stay positive, and keep your appointment with Father! I'm praying for you.