Your poor pussy cat, a new baby is a lot to cope with at 15 years old, I'm not surprised it's weeing in the house. Probably arthritic and incontinent to boot.
It's going to get harder for the cat, not easier, once the baby becomes a toddler. I've been through this with my elderly female cat. She'd been a rescue cat and I first had her when I was single, then coped with a new DH and a house move, followed by another house move, a new kitten and then DD1 came to live with us aged 1.
She coped with all of it until DD1 came. She couldn't deal with the stress and over-groomed and I had to keep taking her to the vet for a steroid injection to keep her as calm as possible. Finally she developed other health problems, probable thyroid problems, dental problems (she'd suffered with gingivitis over the years), in the end she stopped eating.
We knew that she was never going to be happy in our house with DD1, sadly, and we couldn't rehome her so we had her pts aged 13 and a half. She'd been such a brilliant pet, but it was time to take responsibility myself and put her out of her misery.
Your cat should not be outside at 15 and not well. It can't be happy not being able to get to the litter tray. Don't try and rehome it, make the best decision for your pet.