“that the baby’s genes...would be passed on from a set that the father’s body contained”
Most likely, but not necessarily.
Half the chromosomes (that contain the genes) have to be paired from the father, and the other half from the mother. Of course, whether the chromosomes that were paired contain genes that were also dominant in the father, is randomly decided, but nevertheless, half the genetic instructions comes from the father's body, where the specific genes may have either been dominant or recessive, in his body. There is no way a mother can provide more than 50% of the non-sex-determining chromosomes that are paired.