“When a man takes a wife and marries her, if then she finds no favor in his eyes because he has found some indecency in her, and he writes her a certificate of divorce and puts it in her hand and sends her out of his house, and she departs out of his house, and if she goes and becomes another man's wife, and the latter man hates her and writes her a certificate of divorce and puts it in her hand and sends her out of his house, or if the latter man dies, who took her to be his wife, then her former husband, who sent her away, may not take her again to be his wife, after she has been defiled, for that is an abomination before the Lord. And you shall not bring sin upon the land that the Lord your God is giving you for an inheritance." Deut. 24:1-4
This is the reference to not remarrying an ex-spouse. However, it is quite specific that it only applies to a divorced spouse that has remarried, then the new husband dies, and the wife goes back to the first husband.
The real question is - Does it apply to us today? I'm inclined to believe that most things like this in the Torah (the first 5 books of the Bible) are for a specific time - the conquest, and to a specific people - the Israelites. Contextually, it would be wrong to take something God commanded to the Israelites 3500 years ago, and say it necessarily applies to today.
For one thing, the whole purpose of this, is to prevent the first husband from being "defiled." Well, as Christians we are under the blood of Christ, and defilement was more a term of the sacrificial system of the OT. However, I would not object to anyone wanting to apply this passage to their OWN life. But we are not in charge of judging others esp. if they are not Christians.
Which brings me to my final point. Broken-hearted, are you trusting in Jesus Christ for your salvation? Because you are angry, which God considers a sin, up there with sexual immortality and sorcery. .
"Now the works of the flesh are evident: sexual immorality, impurity, sensuality,20 idolatry, sorcery, enmity, strife, jealousy, fits of anger, rivalries, dissensions, divisions,21 envy, drunkenness, orgies, and things like these. I warn you, as I warned you before, that those who do such things will not inherit the kingdom of God." Gal. 5:19-21
Notice the phrase "fits of anger." Other versions say, "outbursts of anger" "wrath" "fits of rage." Please note that in a sin list, it is a legal document. No one thing is worse or better than another. Look at all those negative things. I only point this out, because many people do not know that being angry is just as bad as all those things like drunkenness and idolatry, orgies and sexual immortality. (And I say this having gone through having to learn this hard lesson myself, and praying for God to change me over a long period of time.)
I also see that you want to control your father. That is also unbiblical. Only God is in control. And while this whole arrangement is obviously extremely distasteful to you, you do not have biblical grounds to make your father do you will. Instead, pray for this new/old wife that she would find God and God would change her.
I am sure you have made your feelings know to your father. As much as it hurts, it is time to move forward. Live your own life, and pray that this woman will accept you and the rest of your family. I am sorry you are going through this, but the only answer is to believe in God for salvation, and trust him for what is going to come out of this situation.