But the problem is:
is this a true life estate. A life estate is created within the deed itself. It doesn’t sound like this was created in such a manner since the grantees sign nothing when accepting a life estate deed.
the op needs to refer to whatever this agreement binds the parties to and deal with that.
from what I’ve read here I suspect the absent owner won’t likely be held liable for anything. Why the op believes the other owner should share in the expenses where the elderly parent and the op are the only beneficiaries of the deal is a bit puzzling. Op receives the benefit of housing while the absent owner receives nothing.
payrolguy; while the op may not find statute to state the life tenant is liable for taxes (although there may be. I haven’t actually checked) op will find law (case law) showing the life tenant is liable for the taxes as well as normal upkeep of the property. I suspect the problem here though is it doesn’t appear to be a typical life estate and the agreement spoken of is likely to play a large part in what any party is liable for.