That is so hard to say the words that mean that Your Beloved Companion will no longer be there, no longer be a part of your life.
I would wiat until the 15th, and maybe try some Kitten Food to see if the extra protein helps poor Sunny.
I wouldnt push as your Mom may resent you telling her to have her friend Sunny put to sleep.
We are praying for Sunny, that he can recover and has more time left.