JOEL - Both of these concepts have been made known more clearly to us through latter-day revelation. I think your mother already knows that the Bible does not specifically refer to these things in those words.
Isaiah does talk about the time when He(God) will defer his anger and will eventually gather his people through the assistance of gentle kings and queens (Isaiah 49:23) who, we assume, are the same people of "the church of the first born" that are talked about in D&C 76:53-58, refering to them as kings priests, and gods.
Our devine potential as gods is explained in Romans:
"For as many as are led by the Spirit of God, they are the sons of God.
For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father.
The Spirit itself beareth witness with our spirit, that we are the children of God:
And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with [him], that we may be also glorified together.
For whom he did foreknow, he also did predestinate [to be] conformed to the image of his Son, that he might be the firstborn among many brethren.
Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified." (Rom. 8:14-17, 29-30)
Being joint heirs with Christ means that we can receive from God the Father everything that Christ receives. Being glorified together means we can become gods in the same way that Christ is a God.
Jesus told us, "Be ye therefore perfect, even as your Father which is in heaven is perfect." (Matt. 5:48) How can we become as perfect as God is unless we ourselves become gods also? Jesus would not have asked us to do something that is impossible.
And He also said:
"The disciple is not above his master: but every one that is perfect shall be as his master."
Jesus is our master(John 13: 13-14), therefore if we strive to perfect ourselves we shall be as Jesus who is God.
In biblical terms, those who are worthy to share in all the power and glory that God himself has are called "gods": "Ye are gods; and all of you are children of the most High" (Ps. 82:6; John 10:34-38).
In regards to the question on marriage; when God gave the priesthood("keys of the kingdom of heaven") to His disciples He told them, "whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.(Matthew 16:19)
Therefore any marriage ordinance they performed for a couple using priesthood authority would be bound both on earth and in heaven.
Later in Matthew Christ speaks of the eternal nature of the marriage covenant when He says:
"For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh? "Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder. (Matt. 19:6)
In civil marriage ceremonies unions between men and women always carry the proviso "until death do you part" clause. This is a direct act of man putting asunder something that in God's eyes should be eternal. If God says marriage should be eternal then it must be necessary to enter into His kingdom of heaven.
It is important to believe in and have a testimony of latter-day revelation and the prophet Joseph Smith in order to accept what we believe in the church regarding these two subjects. Your mother either lost her testimony of that or never had one in the first place. Without that there is nothing you can say that will satisfy her. Put her mind at ease by telling her that God has already forgiven her for bringing you into the church.