I have done both.

Interstingly enough, the maternal incubation worked better for me last year than my incubator!

I had a heat wave pass thru and the incubator went into the 100s. The eggs didn't make it, but the mother on her eggs knew what to do.

But, the mother has returned to her original size and not much more.. so taking the eggs away does have its advantages if you are looking to bulk your females up.