Honestly OP you have a baby under 6 months and you're pregnant. Take the help.
Running around after a non mobile baby is hard. Running after a mobile over having pregnant is even harder, and doing it with a screamy newborn is a nightmare. It's understandable you aren't on to of doing it all alone as DH is "too busy" so it's absolutely fair he essentially gets someone covering some of his duties.
Covid unless you're isolating, I'm not sure someone in your house CLEANING puts you at more risk than general life
I’m on Mat leave don't book anything early so you have plenty of time to get ready, but you presumably are taking DS out for a walk etc at least once a week?? Even with morning sickness, it won't do either of you any good locked up in the house every day
DS screams at strangers all the more reason to safely expose him to faces
DH works shifts he's a grown man, he can suck it up. How often does his shift pattern repeat?
Me cleaning up gross personal stuff like half eaten food, nappies and dirty pants do you currently live in a sea of dirty nappies and pants? Get a nappy bin, take your underwear off near the washing basket, pick up plates of half eaten every time you go into the kitchen. And she's coming once a week / fortnight, not every morning at 6
£150 per month so about 10 hours a month? I'd cut it down to fortnightly and if DH kisses his job, you stop using her
Your baby will be in the floor crawling etc soon, floors need mopping, nappies need moving etc. DH sounds like he has a good plan