Oh, Blue
it sounds like you're really struggling. Please remember that at least part of that feeling is sleep deprivation and hormones; you CAN do this, honestly. Here are a few suggestions:
Look up a few key phrases/ask your DSD to write some down. These could include 'How are you?', 'I am fine/tired (!)', 'Would you like tea?', 'Please hold the baby' etc. That's so you can recognise her replies and make some remarks yourself.
Use Google translate to look up more complex info like how you like tea 'Blue's tea: milk and 1 sugar; DSD's tea: black etc', then maybe print out and place in the kitchen. In fact, maybe you could write a whole introductory paragraph and run it through Google translate. Include a few sentences per child, such as 'DD wakes up at 7am and eats cornflakes for breakfast. She loves Shopkins. Dbaby wakes up very very early and likes jumping up and down' etc. Might just give your MIL a bit of useful info, and will show willing on your side.
Don't take anything seemingly insulting too seriously; the language barrier plays tricks on us, esp when we're stressed. If in doubt, assume she means well until proved otherwise.
Don't rely on your DH for emotional (or indeed much practical) support; I don't imagine he will give any. It's sometimes easier to cope knowing this up front. If you plan to do all this yourself then you can't be disappointed when he lets you down. Don't bother discussing your plans with him, he will pooh-pooh them as unnecessary - because they would be, for him!! Necessary and helpful for you though.
You can do it, honestly. Good luck 