Hey S.,
Something I have learned about discerning God's will is that sometimes He does give us the choice. This may be why you can't hear a clear answer - because God is telling you that He is pleased with your heart, he knows that your motives are to give Him glory in all that you do, and you can do all things (in any department) with Christ who gives you the strength. It is kind of like Joseph, no matter what situation he was in, he always rose to the top because of his faith. Maybe that is the situation you are in.
I believe that the Lord wants the best for our lives and the lives of our families. Also, there is a verse, I can't remember where, that says as much as it has to do with you, keep peace with all men. I would go to your supervisor and thank her for the opportunities to learn under her. Just explain that you would like to further your experiences, but that you will always be grateful to her. That takes care of your part of the deal. I believe the Lord can take care of her heart towards you.
I hope all goes well, and as soon as I get done typing I will say a quick prayer for you. Blessing to you and your family. I'm sure your faith is a blessing to all those around you!