I can't see this issue straight because I am close to my family and speak with my mum every day on the phone but several things stick out to me:
He is rude to them or withdrawn 40% of the time- this is absolutely pathetic! I don't always love spending time with my IL's but I would never ever disrespect them by sulking or looking withdrawn. Basically he is spoiling one or two events a year by his behaviour and he doesn't even have to go to that many.
I don't find 5/6 times for contact much in a whole year. That's less than every two months. Again- politeness and courtesy is not too much to ask infrequently especially when you are exceptionally nice to his mum for a 9 week period.
He is also utterly hypocritical about being happy for your mum to be a childcarer and then bitch about her being around all the time/not liking her. What an insult to her kindness, she has saved him tens of thousands of pounds and he doesn't even like her. I would be seriously thinking about stopping this arrangement and calling his bluff.
If he genuinely feels the family needs rebalancing and you need to spend more time just as a nuclear unit, then he should stop his own mother coming for over two months, pay for a nursery and stop your mum wasting her time contributing to your family unit.
My husband sometimes finds my family a bit claustrophobic, and doesn't attend every family event, but he is ALWAYS kind and polite to my family when they visit or vice versa and would never ever make them feel unwanted. He knows that my happiness is to a large extent dependent on their happiness and doesn't make me choose between them. I also support him with his family which includes long holidays with them which I might prefer to spend elsewhere.
I suspect your husband is dissatisfied with his life in general, and is looking in his middle-age grump at possible objects to blame, so has fixed on your family- my guess is if you stopped your mum coming around, and spent far less time with them he would still be unhappy and critical, what do you think?