There's a misperception that a "rule" allows brides (and new moms) a year to send thank you notes. That's not true--check etiquette books. The rule is that it's acceptable to send a GIFT within a year after weddings. The thank you notes should still be sent within a couple of weeks of receiving the gift.
That said, I agree with the other moms that it's better to send the thank you notes late than not at all. Tell the people how much you love and use the items they gave you for your baby. If you had already written the notes, but forgot to mail them, add a P.S. saying this.
Most people can understand a new M. letting a few things fall through the cracks during the early months of little sleep and so many extra things to do with a new baby. Most of us have done the same thing ourselves at some point in time!
As for the former friend who hosted the shower, you never know if your note opens the door to mending things and resuming the friendship. Even if you don't want that, it leaves you taking the high road and having done the right thing. I agree with others who said that you should keep that note simple, and thank her for the kindness, and not address the falling out of your friendship.