What exactly would be your reasoning for continuing with your former teacher in any way ? Would it be for her, or for you ?m1469
Discuss it with your new teacher first of all. Many teachers would be offended, but she might be okay...perhaps if your original teacher were "subcontracted", as it were, to help you with certain things...this would only work if your new teacher trusted the old one, of course. Whatever you do, don't go back to the first teacher without the new one knowing and approving.
I am afraid i won't be able to tell themif i took lessons with both of them. Doing so will ruin so much the relationship between me and them.