I just had to give up a cat myself. She wasn't getting along with the cat that I'd adopted before after trying for 6 months give or take. I cried. It was hard. She was also special needs, and the added stress wasn't conducive to her health. She was returned to a wonderful woman who knows how to take care of her at SMAWL (smawl.org).
I also have a cat that eats plastic. There was an occasion where we were convinced he had swallowed some, and it wouldn't pass. We took him to the emergency vet for the removal of the obstruction, and ended up spending $2k on a fruitless exploratory. Turned out he just needed a good dose of antibiotics; he was back to normal once he came out of the anaestesia. We've always just made sure that plastic is always picked up or put away, and have trash cans with lids that snap shut for things like that. The other trash cans are strictly for non-plastic items, unless you can cram the plastic into an empty soda can in there or something like that. It takes some adjustment, effort, and time. I can appreciate not being able to handle that, especially with a new baby. You don't always know what to expect with a new child, and unfortunately the child's health can outweigh that of a cat. Fortunately, we have groups like PAWS, SMAWL, and Second Hope Rescue. I'm sure there's more, and a good way to find them might actually be through petfinder.com. Plug in your zip code and all or most of the adoption agencies will pop up with their animals and contact information. Best of luck. I know it's hard to give up a pet. It's better than seeing them put down.