To be honest, I’m struggling to understand some of the details you’ve written.
“Problem is he does fine at home but seems to fall struggle in school and was hoping to close the gap between the two.”
If his report at the end of Y3 was that he was meeting expectations in all areas, and you’ve not had any feedback so far in Y4, how do you know he struggles in school?
It is great that you are helping your DCs with their spellings and times tables at home, and it is also normal in my experience for a parent to ask another parent for a copy of that week’s spelling list from time to time.
I do think that by Y3 and Y4 you can get a lot of information from your DCs if you ask them a couple of questions every day. If they are not very good at remembering whether they got a reasonable score in a test, or which spellings they got wrong, this is something you can work on with them by asking them each day and encouraging them to remember this information as they should expect you to want to know it when they come home from school.
I consider myself an ‘engaged’ parent but it is very rare that I contact the school – their teacher has 30 children, Covid has meant some are behind – they are busy enough without parents hassling them. I have good conversations with my DC every day, and I have occasionally looked up curriculum expectations for each year from the gov.uk website. Spelling lists and suchlike. It is easy to work out whether they are working on the things you would expect for that year group.
You can also find more activities on BBC Bitesize, Nrich (maths games) as well as some paid sites if you want to do a bit extra, or you could buy the relevant CGP workbooks for their year group and work through them with your DCs at home. You have chosen to engage a tutor for one of your DCs. That’s great if you feel it would be helpful, but it doesn't necessarily follow that, just because that DC is benefitting from extra help, the school is failing him.
You are now telling us that you have multiple issues with the teacher and this is just one of them, and that the teacher doesn’t seem to have control of the class. The issue with one of your DCs sitting next to someone disruptive is something you can complain about if you feel it has been going on too long and is causing your DC some upset, but has your DC tried talking to the teacher about it first? I always encourage my DD to try to deal with it herself by talking to the teacher. It’s a good experience for her to speak up about an issue – much better than a parent having to ‘complain.’
In brief, I think you might be expecting too much from the school. However, as you clearly feel so strongly about it, maybe it would be better to move your DC to a different school? It sounds like you don’t trust them to do a good job. You may be right – maybe another school would work much better for your family.