Did they go to the bathroom outside prior to the hardship and change? Or have they always had accidents in the house?
Is house-soiling the main issue that has cropped up with them or something else?
Honestly, this will be very hard for you and your partner since these are VERY young dogs. It won't be easy for them to have long periods of being alone in a house. Do you have a crate for them to contain them in during the day so their accidents are contained? You may need to try crate training again.
It seems that this is really hard for your partner...he is balancing work and two puppies...that is no easy feat. Not only that, he is most likely very stressed with you being in the hospital. Doing this alone is most likely very tough on him.
Is there some way that you guys can find a temporary foster home for the pups? You may not be in a good place to have them right now, but maybe someone can help take care of them for a time? Or maybe you can look into a dog walker for during the day so your partner doesn't need to worry about them too much (but that costs more money and I am always leery of who I let in my house).
I hope you are alright! Hang in there and get better!