Is my second marriage to my ex-wife valid, especially since she married another man with the intention of making herself lawful (for me), then was divorced from him, knowing that she married the second man without the permission of her guardian (who is non-Muslim), and I fear the invalidity of the marriage and feel guilty?

What you did, introducing the woman to Islam and bringing her into it, is good, as is your marriage to her. However, you erred by committing zina (fornication/adultery) with her. You must make sincere repentance and be careful not to fall into such a sin again.

If you have irrevocably divorced the woman with a major baynunah (final and irreversible divorce), she is not permissible for you until she marries another man with a valid marriage, he consummates the marriage with her, and then he divorces her or dies.

The wali (guardian) is a condition for the validity of the marriage. If the marriage contract was performed according to the madhhab (school of thought) of Abu Hanifa, then it is considered valid.

Live with your wife honorably. Since she is new to Islam, it is especially important to treat her well. Be wary of divorce due to its dire consequences, especially with the presence of daughters.