In this post, I'm using that words "landlord" to refer to the non-resident executor,
and "occupant" to refer to the resident.
It can be helpful to understand that when lawyers say "land",
the term means not just the physical ground, but also all and any buildings on it.
I'm afraid it isn't.
The term "an activity taking place..." has no meaning.
Less riddle-laden language will help.
Thing being, that "an activity" could be anything from entering to make repairs,
through to having a large party at the premises (eg your nephew's 21st in the large garden).
So, I'll take a wild guess here...
Are we talking something like
Executor 1 (occupant): "Yes, you can come and
<make whatever repairs> / <do whatever maintenance>
Just don't come in the house."
Executor 2: "F**k you. As the executor, I'm effectively your landlord,
so I can go anywhere I want.
And if I want to use the bathroom while I'm <fixing the decking>,
then I can, no matter that you say."
or maybe
Yes, you can have my nephew's 21st in the garden.
Just don't let them come in the house."
Executor 2: "F**k you. As the executor, I'm effectively your landlord.
And if I want to let my party guests use the inside bathroom,
then I can, no matter that you say."
That's more like an occupant exercising their right to (mostly) exclusive use
(which right, by the way, extends to the boundaries of the property, not just to the dwelling itself).
I don't see the landlord being right on either count in either of the above (wild-guess) scenarios.
I don't see here a landlord gets to "stretch" a consensual, conditonal, specific purpose entry
into a general right to enter the house.
Similarly, I don't see an executorhsip as creating a right to, say, enter and inspect without notice,
let alone to, say, have a private party in what is, effectively, somebody else's back yard.