Adenine (A) and Thymine (T) are base-pairs, alongside Cytosine (C) and Guanine (G). Only A - T or G - C are base-pairs in DNA strands, you will never see Adenine (A) and Cytosine (C) together in a DNA or RNA strand.
The children were given the recessive traits from their mother and the dominant traits from their father because the genes mix when they have children.