Yes, yes it is what everyone who cares for someone with PSP suffers with.
I never found the answer. You find yourself running on empty because of the lack of sleep. I found one solution it helped a little. Insist on a rest for at least an hour , say after lunch, for both of you. Taken in separate rooms with no disturbing from anyone. Just having that space to snooze or be quiet gave me the energy to carry for the rest of the day. Try it.
I send all my thoughts to you and try to book a respite break.