Cordelia, I am very sorry for what you're going through. It's a tough thing, this talking to family members about the truth when you don't agree with them.
Yes, regardless of the conversation it is likely that the relationship between you and your father will never be the same. My prayers will be with you. As I'm sure the prayers of others here will be as well.
I will tell you what I do in regards to praying. I mostly pray to the Father. I try not to use Jehovah, not because I'm in staunch disagreement over the name, but because Jesus said that I should address my prayers to 'our [my] Father who is in heaven'. The Bible clearly shows that we are all God's children and thus have a right to call him our Father.
I feel that it is appropriate to pray to Jesus. I don't do it very often because I still feel weird about it. I think about all the reasons given here so far; like, when Jesus was on earth we [humnas] talked with him, when he was resurrected we [humans] talked with him, so why would we now not talk with him. Also, he is the head of the congregation (ephesians 5:21-27) and I can not bear to think that God put Jesus in charge yet will not allow me to talk with him.
I found the following at a Carm.org and it makes an interesting argument as well:
Jesus said in John 14:14 , "If you ask Me anything in My name, I will do it." Therefore, it would seem safe to say that we can pray to Jesus and ask Him to answer our prayers. Also, we can see further confirmation of this by looking at the phrase, "call upon the name of the Lord." In the Old Testament that phrase is used only of God and it includes the meaning of worship, adoration, and prayer. Psalm 116:4 says, "Then I called upon the name of the Lord: 'O Lord, I beseech Thee, save my life!'” What is interesting is that this phrase is applied to Jesus in 1 Cor. 1:2 , "to the church of God which is at Corinth, to those who have been sanctified in Christ Jesus, saints by calling, with all who in every place call upon the name of our Lord Jesus Christ, their Lord and ours." Paul obviously knew the significance of the phrase, which included prayerful appeal, and applied it to Jesus.
In 1 Cor. 1:9 it says, "God is faithful, through whom you were called into fellowship with His Son, Jesus Christ our Lord." The word "fellowship" is the Greek word "koinonia" which is also translated as the word "communion." 1 Cor. 1:9 says that we are to have an intimate fellowship with Jesus. That is fine. But, how can we have fellowship with someone we never talk to? Therefore, this verse can also be used to support the idea of praying to Jesus.