You're mixing up a whole pile of concepts there!
"administrator of an estate" would usually be taken to mean an administrator of the estate of a deceased person who died without leaving a will.
Do you mean:
My parents are elderly. The house, the sole asset, is my father's sole name. We need to make my father a Ward of Court and I will act as his committee. ( Or we intend to register an Enduring Power of Attorney and I am the Donee?)
Would I have capacity to sell the house?
The answer to that is yes, you would in either of the two scenarios above.
Or are you worried that one might die before the house is sold and therefore should the property be put in to their joint names?
Maybe you could re-write the query to make it a little clearer?
And can you deal with what is to happen to the non owning elderly person if the house is sold?
mf