Needs full stop after box. And I'm wondering about breaking the lines into two, like this:

Aside from the splendour
of portraits fine
And chandeliers
that glitter and shine

There are toys and dolls
and well-thumbed books
In the pleasant nursery
that overlooks

The formal gardens
and the well-trimmed box.
Here played the children
whose wealth and looks

Were not enough
to steer them clear
Of the fateful challenges
of the coming years.

Still unsure about 'pleasant' and, to be honest, the feel of the whole thing. I don't know that I've conveyed the pathos of the place. Perhaps more detail would be needed - or some illustrations?

Of the <something> kids whose wealth and looks

Were not enough to maintain such style
In the face of War and .....

or

Were not enough to keep them clear
Of the challenges of the coming years

This is getting closer, though I'm not satisfied with repetition of looks / overlooks.  However:

Aside from the splendour of portraits fine
And chandeliers that glitter and shine
There are toys and dolls and well-thumbed books
In the pleasant nursery that overlooks
The formal gardens and the (well-trimmed) box
Here played the children whose wealth and looks
Were not enough to steer them clear
Of the fateful challenges of the coming years

'Pleasant'? 

I'm happier with 'here played' but less so with 'fateful'. 

I'll have another look at this after the weekend, when I shall be busy at the NATE Conference in York.

So having got over some 'glitches', I'm looking at the 'where'

… in the nursery that overlooks
The gardens

Then adding a couple of adjectives - box rhymes nearly enough with overlooks

In the little nursery that overlooks
The formal gardens and the (well-trimmed) box

and back to the 'who':

Of the wealthy kids whose wealth and looks
Could not safeguard the - what?

Or, better without the repetition of wealth. Not happy with safeguard:

Of the … kids whose wealth and looks
Could not compete with - ? -

Not quite seeing the whole picture yet.

The poet is back in residence.   Working on a few little reflections on travels just undertaken.   First off I was thinking about the family who lived in one of the grand houses in Cornwall and were hugely wealthy and influential around 1900. And then the family fortunes declined dramatically.

Amidst the splendour of portraits fine
Chandeliers that glitter and shine
In the nursery there he  / there are well-thumbed books
Read by the - who? - children?

Add a couple of words/beats to the lines:

Aside from the splendour of portraits fine
And chandeliers that glitter and shine
There are toys and dolls and well-thumbed books

Perhaps leave who till later and deal with where

  -in the nursery that overlooks / the gardens

I'm going for an old-fashioned rhyming couplet approach. And why has the font just changed?