15 months is young to try to "seriously" potty train, but if you have room for it in your bathroom, put an extra potty chair in there. If the little one demands to be in there while your oldest is trying to go, you can require that she sit on the potty. I've heard that when you try to train 2 children together, they both figure it out faster. The 1 year old may only go by mistake, but celebrate anyway! You may be fortunate enough to have them both potty trained by Christmas!
If you don't have the space for this, I like the "Tub Time" idea. Who cares if she get 10 baths a day. If it keeps her busy and out of trouble, let her have fun. You don't have to actually wash her each time, and soon enough the weather will be warm enough to just let her play in the water cold.