A: How long should it take?
B: How often should it happen?
C: Does the child's race depend on your infection at time of birth, or conception, or neither(depends on the dad)
On C, I feel it would be odd to go with the father, there's no reason for any super fast nanite infected spawn to ignore any further nanite infestations you came across, including the ones giving the form you have now.
For A: 3-6 days is my gut hunch.
For B: Once per game is more than enough I think but people like going kerazy. Still, I can do a lot WITH the kid if I limit it to one spawn. Other option would be to allow as many as you want but only the oldest 'counts' for specific things, like taking the tyke out adventuring.
