As painful as it is to read your words, I must say at the outset that I couldn't be more pleased with being afforded the opportunity to respond to you and your most difficult circumstance.
Many years ago, I attended a rabbinical gathering where the subject matter expert advised rabbis present to consider sermonizing on the painful reality of estrangement within the Jewish family. At the time, I must admit, I did not see what the 'big deal' was. Later, I came to understand just how widespread this awful phenomenon has become.
I chose one Rosh Hashanah to speak directly to a congregation on this subject. The sermon had just the right impact, even causing a congregant to approach me with the request for a copy of my words which she wanted to send on to her son, who was experiencing the pain of being estranged from his children.
I wish to speak directly to your circumstance and offer you some mussar--values and ethics, Jewishly.
You are clearly attempting to justify your attitude and treatment of your father (and mother). This is understandable, but unacceptable in Jewish tradition. Have you ever wondered just why in the Asseret Ha-Dibberot--the so-called 'Ten Commandments' or Decalogue, the mitzvah/commandment of Kibbud Av va-Em, the Honoring of Parents is highlighted and even records -unusually - the reward for this mitzvah's observance?
Let's look at the commandment: "Honor your father and your mother: that your days may be long in the land which God your Lord gives you." (Book of Exodus 20:12) In a slightly different form, the Decalogue is repeated in the Book of Deuteronomy, Chapter 4, verse 16: "Honor your father and your mother, as God your Lord has commanded you; that your days may be prolonged, and that it may go well with you, in the land which God your Lord gives you." See also, "You shall fear, everyone, his/her mother and his/her father." (Book of Leviticus 19:3)
I like to refer to the 'Ten Commandments' as the 'biggies.' It is interesting that Maimonides has his own categories or classification of mitzvot, including those commandments which are intuitive and do not require a Divine revelation, and those which are not intuitive, thus requiring revelation in order to learn that these are Divine requirements placed upon us at Sinai. It may sound counter intuitive for us to hear that in Maimonides' society and times he could categorize Kibbud Av va-Em--Honoring Parents in the intuitive category, that it would not have to have been revealed to us as a Divine imperative.
To Maimonides, honoring of parents and teachers is a part of the Creation and nature, as designed by the Supreme Creator of all life.
You present several reasons for why you question whether you have the responsibility to demonstrate respect for your 90 year old father and whether you need to mourn your father when the time will come. Among these cited reasons are: his remarriage following the passing of your mother and his wife of around 50 years; his choice of burial not with your mother; your lack of feelings of love for him; your belief that he does not love you; not having spoken with him for years; the painful experience of reopening old wounds, and your feelings of being abused in one fashion or another.
You seem to believe that according to Judaism that only parents who have earned your respect in accordance with your judgment and needs, are deserving of being honored, especially to be mourned upon their passing.
This assumption is completely wrong and very un-Jewish. The commandment is explicit: a parent, whether father or mother, is to be honored. A parent does not have to do anything specific to be deserving of your respect. Yes, a parent has responsibilities towards a child, but nothing will absolve you of demonstrating honor to your parents.
Who has the right to decide for your father, whether he can or cannot remarry after the passing of his wife, or even after a divorce? No one.
The Sages of Israel are explicit in their interpretation of the Torah in this matter, as presented in Rabbinic literature. We see this presented in the Mishnah and Talmud in several tractates including: Kiddushin, Sanhedrin, Ketubbot, Bava Metzia and Yevamot.
A pivotal source on the subject of Honoring Parents is to be found in Maimonides' Mishneh Torah, his compendium of Jewish Law. This is in the fourteenth book, Sefer Shoftim--Judges, Laws of Mamrim--Rebels, Chapter 6.
Law One: "It is a great positive precept to honor father and mother; so too, to pay reverence to father and mother. Scripture considers the duty of honoring parents and revering them, to be equal to the duty of honoring and revering God. It is written: 'Honor you father and your mother' , and it is also written: 'Honor God with your wealth' (Proverbs 3:9) ....
Law Three: "What is the distinction between reverence and honor? Reverence signifies that the son must neither stand not sit in his father's place; he must not contradict his father nor decide against him . . . What does honoring signify? The son must provide his father and mother with food and drink and clothing, paid for by the father. If the father has no money and the son has, he is compelled to maintain his father and mother as much as he can. He must manage his father's affairs, conducting him in and out, and doing for him the kind of service that is performed by servants for their master; he should rise before him, as he should rise before his teacher...."
Law Seven: "To what lengths should the honoring of one's father and mother go? Even if they took a pocketful of gold pieces belonging to him and cast it into the sea right in his presence, he must not shame them or scream and be angry at them; instead, he should accept the divine decree and keep silent...."
Law Fifteen: "A person is obligated to honor his father's wife, even though she is not his mother, all the while his father lives, for this is included [in the commandment] of honoring his father. So, too, he must honor the husband of his mother all the while his mother lives; however after her death he is not obligated ...."
I have chosen to highlight but a small selection of the details enumerated by Maimonides, there is so much more.
Under no circumstance is it Jewishly permissible to ignore or rationalize away one's obligation to honor a parent. Most certainly you are obligated and commanded to mourn the passing of your father. This may be a challenging, but with God's help you will succeed in fulfilling your responsibilities.