I get along great with my MIL. Not once has she come over to our house to 'do our gardening.' You may not have said it was messy but you implied it because otherwise why would you need to do their gardening? She has definitely never replaced anything in my house. I would be very offended if she bought me a new bath mat. My MIL also doesn't try and go around me all the time by only communicating with her son, she makes sure that we are all on board.
You sound arrogant. You sound like you know everything and have everything and that they are struggling so hard and NEED you. They don't. You only perceive them as struggling. Leave them alone. My MIL has never once implied that we need her help or that we are struggling. All I get is praise and trust me when I say that its hard lol but I know that if I need them, I can ask. Stop assuming they need your help.
This story has played out so many times on mum forums and it goes one of two ways. You say that your son loves his mummy and will never leave you, okay then she will throw him out. He needs to put his wife before you or she will leave. If he puts her first, he WILL reduce or cut contact with you. Why would a mother want to force her son to make that choice?
Its soo common to hear everything was fine before we had kids. We got along okay and then MIL became so controlling and overbearing once we had children. If I was your DIL, I would have either kicked your son out or refused to have any further contact with you. Your SO told your son to sort her out? She's not an animal or object, she's his partner.
You come from a place of love but you are doing it wrong. Stop assuming they need you. You sound like my parents. Always undermining my confidence with statements like 'you must be struggling etc etc' and also 'we expect you to ask us for advice and listen to it' I laughed at that one. If they don't want your advice, they don't need it.
In regards to the cot and pram, did you just buy what you wanted? The really fun thing to do when having a baby is picking out the furniture and sometimes you want things a specific way. If you just bought them what you wanted them to use (not things that were practical for them or matched their theme) of course she would be annoyed. My MIL has never once bought me furniture for baby. If you had really wanted to help, you would've asked them what wanted (in your budget) or gone shopping with them (without making your opinions known).
My parents have also struggled with seeing me as independent. I have no idea why, I'm 32, have a masters degree, married for 8 years and 3 kids. They still think I need them. It took some arguments to get them to back off and now we are NC because they just can't accept that I don't need them. They constantly still see me as a child. Start seeing your son as a man and a father. Do not offer to do gardening or laundry.
Sorry rambled a bit