Infant of Prague has been in my family for about 50 years. My mother recently received it and everyone believed that the outfit the infant Jesus wore was beyond hope. Mom let me take a stab at cleaning the poor dear. As you can see, I managed to get those 50 years of tobacco stains out of the dress and cloak. Woohoo! Here's how.
I used baking soda, Tide, and room temperature water as a soak. This is what the bathtub water looked like after only a minute long soak.
Once the water looked more like a weak lemonade than the urine color (sorry, but there isn't another way to describe that!) you see above, I left the cloak, dress, and petticoat to soak overnight. The next morning, I washed them all again and then rinsed out the garments to leave them to dry on the shower curtain rod.
The dress is in a bit of tatters but it at least is CLEAN now.