My MIL is a pain about this. She always says "can't you just pump?" I'm like "No." I don't even explain why anymore b/c she is just asking to be a turd. It doesn't help that we 'had' to supplement the first bit with expressed breast milk or that I will be returning to work so I am pumping daily. But both her and my husband's whining about it has made it difficult to get a store ready for me to go back. I finally had to just put my foot down and have a heart to heart with my husband about how we all have different roles in taking care of our new son. He is the designated bath giver and tummy time player etc. And everyone else is there to help comfort and play with baby when you need a break but better yet help you with anything that needs to be done that isn't newborn related. My husband realized he was being childish and started helping more and he's taken up for me with his mom too. He also finally explained to me why he wanted it so bad... He was jealous that if need be I could take care of our child 100% but if something happened to me he couldn't do the same and it made him feel like a lousy provider. He is so more old fashioned than he thinks he is. Just hang in there!
Another thought is when he is spending time with the baby say things like 'oh she loves it when her daddy does X" "look at how happy she is with you". Also, when it comes to the cleaning is saying "thank you for doing X. This breastfeeding thing takes a lot of getting use to and I'm so thankful I have such a supportive husband" I saw this on another post and tried it. It has to be really sincere and only if he hasn't complained right before. But it worked for me. Kill 'em with kindness.