I hope the trial basis works out.
We had to do the same thing - I had two 6yo cats I adopted as kittens when I was single. I loved them so much. But as our lives changed... I got married, we moved several times, then the baby came along at the same time as us buying a house and moving yet again... It was too much. We made it 16 months after DD1 was born. Same reasons as you, except the cats didn't limit it to the room where the litter box was. For me, the deciding factor was when I found a huge puddle in DD1's room where she had been crawling earlier that day. My parents were willing to take the cats, thankfully, though they ended up putting one of them down about 2 years later (she never "recovered"). The other cat is now living with my sister at an old age of 14.
Anyway, just wanted to say lots of hugs. It's such a hard decision and I understand how stressful it is. I don't regret rehoming my cats at all, and I do think they were happier after.