Scrunchiemount, I think you're going to have to play it by ear.
It does sound like your SIL is very anxious and trying to control her environment as she faces the screaming ab dabs of childbirth. She sounds like she needs to do what she's doing.
But it is her decision how she goes from here, not yours, and she seems to have a very different family to yours, so you have to respect that.
Maybe her DH will be able to steer her in a more reasonable direction which will be better for her if she does have depression, but I don't think that will be any of your doing.
At this point I'd ask her is she needs any practical help, and suggest she gets a cleaner to come in so she's not exhausted cleaning up her house for her visitors. Maybe you could help her there?
She may well be having a horrible time with hormones, and my have anxiety/depression already, so anything that makes her feel more in control is better for her and her baby at this time.
She may change her mind after her baby is born as things change then.
Fwiw, I agree with some of the things that twinkles blog link said.
For my first, I had streams of people popping in at all hours (later and earlier than agreed) expecting me to serve them tea, with milk and two sugars (but never brought milk) and meals (if they stayed too long and were a bit peckish) and they stayed for hours, sitting on the sofas, without lifting a finger around the house, or even making me a cup of tea.
Someone came with her two kids who had raging tonsillitis and nits.
Someone was totally miffed as she rocked up 45 minutes late and I wanted to breastfeed, and she was too embarrassed, and upset that my baby needed quiet, so my babe had a meltdown with hunger (as I delayed the feed for 20 minutes until I couldn't any longer) and screamed with wind all night.
Someone came at lunch time, empty handed and unannounced, went into the bedroom, and picked up my sleeping baby, waking her up, so I had no time to sit down and eat my lunch with the luxury of two hands! I was starving, but had to quieten down my screaming baby all over again.
It was a fucking nightmare. I do wish I had had two weeks at least where no one visited. Even thinking about those visitors (family and friends) makes me stabby all over again.
I got wise.