If you go back to May, the preparations for occupation of the two rooms 2nd floor back, Granny Shepard, well into her 70s, took several days to clean them and, of course, Nat's took priority, so in the interim Granny had to return to her former lodgings! 
Yes she did ... but she may have willingly taken on the task.
Nat's took priority,
Well we don't know that for certain ...
so in the interim Granny had to return to her former lodgings! 
She may have paid rent in her old place up until a certain date and did not need to move to Richmond Buildings immediately ....
I don't think we can escape from the entry for Monday 16th May: ' Old Granny Shepard sleeps at her lodging tonight, the room not yet being in readiness for her, though mine is prepared for me. Slept in it for first time this night.' [The previous day Nat was out gallivanting with Ann ..... ]
It appears that there is an error in page format of the transcription as a date follows for Wednesday that has not been separated into a new heading but the inference is clearly that Granny's room was not in a state of readiness for her to sleep there until Wednesday night and we know that Nat's mother was very ill at this time - confined to her bed for almost the whole month according to Nat.
So dee-jay, are you inferring that Nat was spoilt?

Maybe Nat had seen Ann the previous day but he does hold down a full time job. He was probabaly too tired to help Granny Shepard clean.

Living in a patriarchal society perhaps Nathaniel's needs/wants were given priority over everyone else's even his old Granny. Maybe she just liked to fuss over him? Also remember he was an only child.
Boys probably weren't expected to engage in such activities at that time. Even my old Gran thought that boys should not engage in domestic chores (something nipped in the bud and not passed down the generations

). Nat admitted a while back that he was selfish (when Mr Galangal(?) gave him a talking to?). It was probably just the way things were in those days and everyone had the same attitude.
I don't think we should judge Nathaniel by our attitudes today.