Hello, I'm so sorry to hear how you are feeling I really am.
I am not asian and don't live in the same set-up with the same pressures and expectations you are facing, so I haven't experienced it first hand. However, I have had asians friends in the same situation expressing to me the same feelings you have. I really do feel for you. I think there are many positives to living and relying on extended family, but clearly also many downsides too. Particularly in your case where it feels everyone is reliant on you yet who do you feel you have to rely on?
I understand how it feels to feel suicidal, anxious and depressed because I experience too. Firstly, please you HAVE to put yourself first. If you are well your baby will be well, and that will make dealing with your home situation easier then too. So you come first. Have you thought about contacting the charity Mind? Find out what resources, support and therapies are available in your area. Also visit your GP as a matter of urgency, you have to be honest with them about your suicidal thoughts - do not be embarrassed. They have heard it before and will not judge you. It is a symptom of depression. I think counselling and/or CBT would be beneficial. I know you say you will not feel better until you leave this house, but in the meantime you can help yourself manage your current situation and that will go some way to making you feel better.
Also, do you get out of the house much with the baby? Ensure every day you both get out for a walk together, schedule a time and stick to it. Do you have any friends you can meet up with on this walk? If not doesn't matter still go. A 30 min walk isn't going to make a blind bit of difference regarding cleaning the house. You DO NOT have to be stuck in the house - you are not a slave. The extended family do not need to understand, they just need to accept. If your MIL throws a fit let her, she'll get over it. It's a 30 min walk out of a 24 hour day. Unfortunately, as with most women and house work, no matter what culture we are from, we can easily be taken for granted and the more you do the more people can expect. Take control back as much as you can - I understand this may be a difficult balancing act so as you don't cause yourself extra stress by creating a family drama. However, keep the longterm in mind and your priorities in mind.
Can you speak to your husband about this? Or is he bound to take his mum's side? Maybe he can have a gentle word with his family, take the pressure off of you by saying he has decided that you and the baby need more time and less stress for a while.
I really hope you can find small little things to introduce into your day that will help you manage your situation better and make you feel better bit by bit. I I hope your husband will understand. Please do as a priority go to your doctor and give yourself 30mins a day just for yourself out of the house.
How are you feeling today?