Basal keikis are usually left on the plant since it gives more of a specimen plant look, and the double amount of blooms can be impressive.
As long as you cut off the keiki when it had a good amout of roots (some people say a total length of 5in, others say at least 3 roots of 3in) there's no reason for it to die. Just make sure that it's potted up in a pot that's adapted to its root mass. As for the mother, don't worry, if you made a nice clean cut it will be fine.
As to why the mother is not blooming, you need to give a bit more information about how you grow it. With what/how often do you fertilize? What sort of light is it getting? Are the roots healthy? That way it becomes easier to pinpoint what may be wrong.