If a human patient's bone marrow was removed, altered genetically, and reimplanted, would the change be passed on to the patient's child?
No. Changes in a person's bone marrow could change the composition of their white blood cells and platelets, which are the cells that bone marrow makes. Bone marrow cells are somatic cells, which means that they are diploid (each has two copies of every chromosome) and are not involved in the process of reproduction. Alterations in somatic cells cannot affect the process of reproduction, so any changes in them will not be passed on. Only changes that affect the gametes (egg adn sperm cells) can be passed on to a child.
The patient who recieves the genetically altered bone marrow would be considered a chimera, an organism that carries DNA from more than two sources - the norm is considered to be DNA from two parents, so your patient, carrying a third form of DNA, would qualify.