How do two parents, recessive and dominant genes and two complimentary nucleotides end up in one DNA?
I think you really need to go back to the very basics and try to understand the DNA molecule, what a chromosome is, DNA replication and mitosis, what homologous chromosomes are, what non homologous chromosomes are, what sister chromatids are, what non sister chromatids are before you attempt to understand meioses. And I would definitely recommend you learn all of these things well before you attempt to understand molecular inheritance, but let me see if I can at least begin to clarify some of your misconceptions.

If you are having a hard time understanding the concepts as written, try looking up the articles on Simple English Wikipedia first. The try to make their articles easier for novices to understand.

There is no such concept as Dominant Nucleotide Bases. The two strands of the DNA double helix are complementary and antiparallel. Genes can reside on either strand.

You are also getting really mixed about recombination via crossing over in meiosis. The chromosomes that are being recombined in the mother are from her parents, so technically the chromosomes that are being recombined are the grandparents chromosomes.

The same is happening when the father produces gametes. The chromosomes from his parents are swapping pieces of DNA. 

At the end of meiosis, each gamete has a random assortment of 23 chromosomes, either from the father or the mother of the adult male or the father or the mother of the adult female. 

The 23 can be recombined meaning that the chromosome is part grandma and part grandpa, or it is a grandmother's chromosome that has not recombined or a grandfather's chromosome that has not recombined. Just looking at the possible ways that 23 chromosomes can randomly assort without taking into account recombination to produce a gamete, there are about 8 million combinations. Add recombination and it gives you a huge amount of genetic diversity.

So those are the haploid gametes. When fertilization occurs the sperm from the father donates its random assortment of 23 chromosomes and the ovum from the mother has 23 randomly assorted chromosomes of its own. This gives you at total of 46; 23 from the father, made up of a random assortment of chromosomes from his father and mother (or chromosomes recombined by crossing over to be part his mom and part his dad), and 23 from the mother with the same pattern of random assortment and recombination.

Also, the double helix doesn't dissociate (come apart) during crossing over [NOTE: for those who know, please do not jump on me for not explaining strand invasion here and the need for homologous sequences for crossing over]. One part of a grandparent's chromosome is exchanged for the exact same part of a chromosome from the other grandparent's chromosome, assuming normal cross over events. The alleles (versions) of the genes in that segment may vary, which is why you have a chromosome is part grandmother and part grandfather.

As for dominant autosomal genetic traits versus recessive genetic traits. A dominant trait means that a heterozygous child will express the phenotype even though they only have one copy of the dominant allele. If it is a disease, then we say the person is affected. If it is a recessive trait, then the heterozygous child will not express the phenotype, so they are not affected by the disease, but they carry the allele and can pass it on to their children. This person is said to be a carrier. If a person is homozygous for a recessive trait, then they will be affected by the disease and show the phenotype. 

As for inheritance, you have to draw the punnet squares. This will show you the different patterns and probabilities of inheritance.

UPDATE

I think that you are getting confused by the idea that you inherit one set of 23 chromosomes from your mother and one set of 23 chromosomes from you father. While this is true, meiosis happens in their reproductive organs before fertilization (for the most part, but the important part happens there and then).

The example of the father is easier. He has two sets of chromosomes, one set that he inherited from his mother and one set he inherited from his father. At the beginning of meiosis all 46 chromosomes replicate. They make an exact copy of themselves and are joined at the centromeres. You have 2 sister chromatids on each of those chromosomes. Now the the homologous chromosomes will pair up, so one of the chromatids on the paternal chromosome (say chromosome 4 from Grandfather's set) will join with a non sister chromatid from the maternal chromosome (Grandmother's chromosome 4). So you have four chromatids from chromosome 4 lined up at the metaphase plate. The two non sister chromatids that are joined will recombine when the kinetochores move along the microtubules towards the poles of the spindle. At the end of all of this you have two cells that contain 23 chromosomes, each with a sister chromatid, however the sister chromatids are no longer identical because one of them recombined with the the non sister chromatid of its homologous chromosome. The thing you must remember is that each chromosome assorted independently of the other. For Chromosome 1 the maternal chromosome may have gone to the left cell while the paternal chromosome went to the right. Then for chromosome 2 you might have the maternal chromosome go right and the paternal chromosome go left. And so on and so forth. The number of possible combinations of how you can arrange two sets of 23 chromosomes is 2^23 or about 8 million different combinations.

During meiosis II the 23 chromosomes again line up at the metaphase plate and they are attached to the spindle by both sides of their centromere / kinetochore complex. When the migrate the two sister chromatids migrate towards opposite poles. Again it is completely random as to whether the recombined chromatid or the chromatid that did not undergo recombination will migrate to the right or the left. Again, there are 2^23 possible combinations for EACH cell.

So you end up with an incredible amount of genetic diversity on how chromosomes are assorted within the gametes. You will still only have four possible outcomes  in the copies of any single gene that you get. You will inherit either your paternal grandfather's copy or your paternal grandmother's copy and you will inherit either your maternal grandmother's copy or your maternal grandfather's copy. That is why if a genetic disease is caused by one gene, it depends on which copies you inherit.