No, you've not quite got your bearings.
As you drive in, you pass between the old caravan sales yard (Glen Caravans) and the lodge at the gate. Just past the caravan yard is a building on your left, inside a small boundary wall - this is the nunnery, Convent of the Good Shepherd, and which, as you note, was reportedly used for refugees. It seems to be a bit tidier than when I last saw it some months back. I have comparative pics, but haven't had a chance to look at them. Whatever, it's still there and untouched, if looking unused.
Looking at the aerial views, you will find this 100 m to the north of the not Easterhill House site. As you'll see from the shot that shows the house, it was well buried inside a small wooded area, and I only saw it when I did because I was exploring the graveyard on foot, having worked my way south after discovering the Polish section of the grounds.
I don't know what you would class as a later construction, but if memory serves me at all, we are talking about Easterhill House being similar to Calderbank House. All I can recall from what I could see through the trees was steep roof and brown walls. There were workers/youths milling around so I wasn't able to sniff around or take pics that time, and didn't expect it to be razed - it certainly wasn't dilapidated from what I could see.
Always the same... write a post expressing ignorance, then find the answer's sitting under your nose...
For your delectation, Easterhill House:
http://gdl.cdlr.strath.ac.uk/smihou/smihou037.htmAnd, no, it was too long ago, and in too many trees for me to swear it is the same building.
Flash Earth lets you use the compass top right to spin the view to try and match the plan with the old view, but with a chunk lost in the trees, and the option of changes over the years, unless somebody can state a rebuild, then your guess is as good as mine :-/