What do I do when my sibling who took over our mother's care will not listen to reason and our mother is suffering?

It's a moot point, really, b/c your sister is unwilling to move your mom to where you live. Furthermore, your mom is being cared for by nurses who are professionals, although you call them 'strangers'. She would not necessarily be better off being cared for by you, nor would she be in better spirits if your sister were home more, since I think you are purely speculating about why she's 'miserable' to begin with, and why she's 'falling deeper into depression.' You do not know what her diagnosis is, what her situation is, and are just imagining she'll feel better if she were to come live with you. Meanwhile, you are 'heavily pregnant, chronically ill and in another country.' It hardly sounds like you are in any position yourself to take on a sickly mother who'd have no insurance in your country!

Your best bet is to go visit mom after your baby is born and see what's going on FIRST HAND so you can make an accurate assessment yourself. Try to get on better terms with your sister so you can have honest, heart to heart talks about mom in the meantime which would make you feel better, too.

Best of luck to you with everything going on in your life right now. Please take care of yourself and your baby and remember that with nursing care on hand, mom IS in good hands right now!

Caregiving is difficult enough without adding:
You are pregnant
You are ill yourself
You do not know what your moms diagnosis is.
You don't know if you can care for her.
And you want mom to move to another country where she has no friends, no doctor and other than you no real support system. Not even going to get into a possible language barrier.
Can she afford private pay medical care here? Or can you afford to pay for her medical care?

I am guessing your sister is well aware of mom's diagnosis.
Your sister got mom nurses to care for her.

The fact that your mom is depressed makes things more difficult, the depression will not improve if she is uprooted from her home.
Is she being treated for the depression?

How do you know she is not eating or talking?
Is it possible that these are indications of her medical condition and decline?

In your profile you say you are taking care of mom in your home and she has osteoporosis, depression. Is this just projection or are you caring for someone else? If so you do not need to add another.
Adding a baby along with your chronic health condition will probably be more than you can handle.
Also I have to ask...what does your husband have to say about bringing mom into the house?

I just can not see this as a good idea in any way.

You describe yourself as chronically ill, heavily pregnant and in another country. Sounds as though Mom and sibling need to work together to do what they can as regard's Mom's needs which are very very unclear. You cannot control the entire world from a world away, and having that world coming to YOU sounds a disaster in the making.
Concentrate on yourself. When Mom calls with complaints give her the number for calling 911 if she is in the USA. When your Sister calls with updates tell her you are sorry she is trying to handle this on her own, but you are a world away, ill, and pregnant.
So sorry. Not everything can be fixed.

Without knowing what your mother's diagnosis is, why would you want to move her in with you? She could need 24-hour care which will be incredibly difficult if you are going to be having a baby. You don't know if you could care for her better without knowing her diagnosis. Paid care may be the best option for her and as you say yourself, you don't know if you could care for her full-time and that is before you have a baby.

Instead of trying to get your sister to agree to move your mother, why don't you discuss her diagnosis? If she is truly depressed, what can be done to improve her mental state? I think moving her is the last thing to consider.

If you’re going to give birth soon and are chronically ill and on top of it live overseas, what exactly would you do if sis did send her over to a country where she doesn’t get Medicare or Medicaid?