I think your DH and MIL sound like they are from the 1950s?!
Your DH is underestimating how demanding it can be looking after a little one- perhaps he could have the baby one day on a weekend and see how he gets on juggling baby and domestic duties.
If the house does really need to be tackled perhaps your DH can take some A/L to help out so you can both get on top of housework. As others say invest in a cleaner for a few months (forever?!) if it’s doable in your budget. Perhaps your MIL could bring a meal over or help with some housework?
Some MILs get a bit weird when they see their DDiL things differently to them.
You sound like you’re doing great mom, you’ve been washing, hoovering, making soup as well as getting out the house. Going to baby groups with a colicky baby is an excellent idea. Don’t feel bad. Happy mum happy baby!
Why doesn’t your DH get more oven ready meals in so it’s easy for you both to grab something. Or between yourself and DH you could batch cook a chilli, a curry and/or a soup, roast a chicken so you have something easy to heat up over the week. Maybe you can meal prep, do a shopping list and get an online delivery so food is all sorted for the week.
Seriously leave your DH with the baby and see how he gets on with the dusting!