Hey there. As a mother of a 10 yo 5 yo and 3 month old, I know for a fact that it does get better.
Whatever the sleeping problem it will improve with age. But I know it's so hard to see that when you are in it. My 3 mo is up throughout the night and does not nap well at all, and it is so hard right now. It feels like it will never end. But I know it will.
I'm sorry your wife is so ill. Sounds like you both have done so well with your lo in spite of that, given how well she sleeps during the day. I wonder if you could get some help with settling at night. Perhaps if you post your routine, someone could give you some suggestions. Is her bedtime perhaps too late? Or maybe she's ready to drop a nap and therefore not tired at bedtime.
Do you give medications for her teething? It can be so hard on some lo's.
I hope it gets better for you soon.