Cat help!

Background- my cat is 15 he’s a male

We have been having issues with him peeing on the tile floors A LOT like he does 2-3 times a day. Now he’s throwing up everywhere, like all the time. Today it was a pink color. He also pooped twice on the carpet today.

We took him to the vet about a month ago. They said he’s getting old and has neurological issues- his head twitches sometimes. Gave him a vitamin B shot and sent us home and said there wasn’t much we can do.

I personally think the cat is miserable and would be more humane to out him down. My mom thinks otherwise and is basically cleaning up cat shit, puke and piss all damn day. I’m really at my wits end with my mom. The cat pukes so much he can’t even meow he’s to hoarse.

He is still eating but everything he eats he just throws right back up. He’s pretty skin, lost 2lbs since the summer.

My question is what would you do if you were in this situation? And what does it mean when a cat is throwing up pink? It’s not his food either.