I don’t think that Alice is going to get ruined by Smokey…but dogs do pick up what other dogs do. I would keep working every day, several times a day, in short bursts with Alice’s training. Keep doing it and it will continue to reinforce what Alice has learned. Try to get Smokey involved with the training too. If you are lucky, Smokey will see what happens when Alice does good, and will start offering up tricks and whatnot to get treats too.
Make sure that you spend time with Alice ONLY and without Smokey so that “jealousy” doesn’t result and Alice resent Smokey for being there. That could spell trouble in the future.
Make sure that you keep Smokey indoors or behind a fence if outside to keep Smokey from wandering off. You don’t want something happening to Smokey. Non-leash dogs can be taught to be leash dogs. It takes a lot of work and training, but it can be done. This is where a slip-lead would come in handy, just to get Smokey used to something around her neck. If she wears a collar, attach a leash to it, and let her drag it for a bit, then remove it. Treat her constantly to let her know that it is ok and it is a positive thing. After some time of this, pick up the leash, hold it, treat Smokey and then let her go. Gradually, you should be able to get her moving with the leash on. Again, it will take time and patience, but it is really important that Smokey be trained.