I 100% agree with everyone saying that you are completely, undeniably NBU to say no, and that you shouldn't have to say anything else.
However, I do have a thought that I haven't noticed elsewhere here (I haven't read every single comment). Is there a chance that your husband is partially behind this by talking about your PND with his mother? There's this perceived & usually ill-applied "she needs a break" idea when it comes to PND; is there a chance that they're trying to help you by "taking the pressure off" and think that you're making it worse for yourself by not accepting it and "struggling alone"? I DON'T agree with them - let me be VERY clear - but I've seen directly this happen to two friends and it took for me pointing it out for them to realise. Both resolved by them having to acknowledge to DP the relatives intent and what they were trying to achieve, and explain that it will only make them feel worse. That yes a break might help, but it's not the baby they need a break from. Sure, if someone wants to cook the dinner, clean the clothes, do the shopping, take their shower, pay the bills, buy the new baby clothes and sort out the nursery, so that as a new mum there was nothing but spending stress free time with baby, that would be great and may ease the crushing, constant "looming dread" sense of PND. Taking the baby; opting out of parenting for the night, isn't the answer and the prospect can stir up or compound feelings of failure, a loss of purpose and loneliness.
I just wanted to offer an alternative way to approach this, since I've seen repeated "no"s be completely ignored by well-meaning but ill-informed relatives sure that they know how to help with PND. Whatever it is, I really hope you get it sorted x