Yup, brand new news to me... so many people haven't seen Friends!
I would hang it in the least offensive/obtrusive place possible and try to ignore it.
If you damage it, she may paint you another.
If you get rid, you'll really upset her.
I do take issue with the idea that artists gifting their art is always all about them though.
That could be true of many people giving all sorts of gifts and is a problem with the gift giver, not the gift itself.
I have given art I've made as gifts, tends to be to people who have bought art from me in the past or expressed an interest and it's rarely a surprise gift! Its always a 'would you like x piece, I won't be offended if it's not your thing' and not a 'tadaa I expect you to spend £££ having this framed and you to display it over the mantlepiece in the living room' thing!
I don't have friends who'd agree to receiving something if they didn't like it though!
(I tell a lie, I once went to fairly ridiculous lengths to find out what someones favourite moth was, relevant to a long running joke/story... and painted it in miniature on a teeny tiny canvas for their wedding. It's been hanging in their hallway with a lot of other wildlife/wild-flower art for the last decade so I'm pretty sure they do like it!)