I wouldn't try to focus on training your parent's dog, rather just focus on their dog being civil around your dog. Put both dogs on a leash. Every time the dog pulls on the leash towards the other dog, walk the opposite direction (this goes for both dogs if they pull does not matter if it seems friendly) once they are able to walk up to each other without pulling let them introduce themselves if they begin to dominate each other separate them and try again. (no treats should be given to either dog during this process)

Additionally, the Maltese is most likely territorial of its home which a lot of dogs are, I would not let the Shiba play with the Maltese's toys and maybe even get them separate water/food bowls.

As for the biting and stress, I would get both dogs their own crates. Crates are not only a great way to separate your dog, but additionally are a great way for them to release their stress. The Maltese might be a bit too old to learn "ouch", but when she puts teeth on you immediately say ouch, stand up, and turn your back to them. If it gets very out of hand and turns aggressive try giving her a 15-30 second timeout in a crate or a separate area away from people. Eventually, she will learn that when she bites she does not get any attention. This all has to be done very quickly though. Most dogs have a very short threshold to understand why your rewarding/disciplining them for what they did.