I am so sorry that this is happening. I know that losing an animal has always been devastating to me. To the point that when I lost my last grey girl, two friends in the mental health field, and numerous others asked if I was really sure that bringing another grey into my life was a smart decision. Maybe not "smart" but the only one I could make, for the same reasons that you state. If the cost paid for the love and the lessons and the pure joy that these animals give us is emotional devastation, it may not be "smart" but it is a price worth paying.
Sending lots of prayers and good thoughts for Mittens and hugs for you both.