I think a lot depends on how close you are to finishing My New Family.
If its not that close to finishing then I would say that alternating updates is probably the more sustainable long term strategy, with the proviso that if you are really in the mood for one update more than the other then you should follow that feeling.
Ive always felt the best way to avoid burn out is to avoid forcing it. If you are enjoying it, that will show in the story.