If this is true, this is pretty negligent. As a former Mormon missionary, this is really weird though. If we needed medical attention we never needed to seek permission, we went and got it. Usually this meant calling and informing them we needed medical attention on the way or after the fact, but we never had to call and get permission.
I'd also like to point out that it is required to take care of any serious dental work before you can even get approved for a mission. This means you need a dentist that clears you and says you will not need any Dental work while you are on your mission. Thus, many people it is often a requirement to get wisdom teeth removed before a mission. If there were any more serious dental issues that required her to get much needed dental surgery, this would have been fairly easy to see. I am serious about this though, the church will not approve you to go on a mission with a bill of dental health with documentation from a dentist that you DO NOT NEED and will not need any anytime in the next couple of years. So, this story kind of raises a weird red flag for me... Can OP explain how she was approved to go?
Also, why would you need to ask the mission president's wife for permission to see a doctor? That is just weird... At the end of the day, you listen to the mission president and only the mission president, not the mission president's wife, as she is not the mission president. Often she'll chat and talk and give advice and share her personal feelings and testimony, but she makes zero decisions regarding what to do within the mission. This is just how it is laid out. That is why I find it really weird that she would be calling the mission president's wife. I suppose it COULD be something weird like the mission president thought he was being nice by letting the female missionaries chat with his wife in place of him for other issues? I don't know...
Also, this story seems kind of sketchy that even though she may have seemed to have been doing better, she wasn't and the hospital released her. Really? Since when do hospitals offer a discharge before checking elevated white blood cell levels and other screens and when they see them being too high, which they would have here, they would not have released her?
Look, maybe this story is true, and if it IS true, absolutely you should take legal action, and this is coming from a Mormon former missionary. But, I am also saying that as a former missionary, there seems to be a lot of weird things about this story that don't make a lot of sense. Can OP link an article mentioning the missionaries death? In Salt Lake City, the official church news publishes any and all deaths that occur from people whilst serving on their missions. I'd assume you could find local news articles too. But, I am struggling to find any news at all about any missionary deaths relating to this girl. There WAS a sister missionary killed recently, in 2015, just early March that died of an E. Coli infection in Argentina. But, nothing about this girl... I checked back 3 years of Missionary death records, and even searched local news in Oregon where this supposedly happened, but I can't find anything.
I am keeping an open mind, so if OP can link something validating this then I will believe it, but I can't find anything...