Yes, I would do it, I would convert if it eases my mother's mind in her last hours.
I would convert to Christianity, even if she wants to witness it in front of a priest.
I would convert, and after she has passed away I'd take refuge in Buddhism once more.
My motivation was clean.
Though this is unlikely to happen, my mother is more likely to ask me to renounce any type of religious binding on her death-bed, she would do that because she is worried about me, thus out of compassion, and thus also for her to have a "peace of mind", knowing that I'll be "ok" after she's gone...
Go figure...
So my vote is YES.
I am actually surprised to see the "NO" is winning, as yontenjamyang stated, bodhisattva vows call for intelligence and skills when dealing with our actions, well, that is under the bodhisattva's vows.