Hi there,
I'm sorry to hear of your grandmother's cancer diagnosis. This must be a difficult time for you and your family and you have my sympathies. The painting would be absolutely doable from the photo you provided but because of the cost of supplies and the particular medium you've requested, I'm afraid it would be difficult to keep the price point to your budget. Normally, something like that would cost more than the price I've requested as well. That being said, I have years of experience in the medium and have worked with it as early as high school followed by oil painting courses throughout my college years. I have two examples up in my profile titled "Oil Paintings" if you'd like to see what some of my past works have looked like. I can complete the work itself in under a week but because oils usually take a while to dry the painting itself may not be ready for delivery immediately (hence the 20 day time frame I've provided). I also happen to live in south Brooklyn but work in Midtown Manhattan on weekdays so arranging a meet-up (to give you the finished work) somewhere in Midtown or upper Manhattan would be doable. Let me know if any of this would work for you.
Kind Regards,
Gunel