On the face of it, I don’t think the DH is being unreasonable to have his mother visit her four-month-old grandchild, or to leave the house for a total of 18 hours over a two-week period. I imagine he does need to work at least a little bit in the two weeks. Not everyone has a job where you can just take that much holiday at once. Of course his mother wants to visit the new baby, and it sounds like it’s a big trip for her, so two weeks is a fair length of time to stay.
That being said, he is very UNreasonable to have put so much pressure on you for the visit. IF he’s a good guy otherwise, I would chalk it up to a poor attempt at humour. Keep in mind he’s probably pretty nervous himself. He’s got just as much at stake as OP in making it work.
OP, one thing you could do is ask your DH to explain your mental health situation to his mother. She may be understanding, but even if she’s not, it doesn’t sound like something you will be able to hide rihhh now. This woman is coming to meet her grandchild, so if you cry, scream, and flee, taking said grandchild away, your MIL is understandably not going to be happy. But if she has a bit of information about the situation she may turn out to be supportive, or at least she will understand what’s going on. She’s had newborns herself, and she may relate to your situation more than hours think.
I know about anxiety, OP, believe me I do. But try to avoid making your fears into a self-fulfilling prophecy. If you feel like your home is being invaded and your blood is boiling, you may unintentionally come off as cold, erratic, or generally difficult. Your MIL is family now, and you should do your best (to the extent you are capable right now) to welcome her warmly and make the effort to connect with her.