If you were a teacher here in the UK lately then you must know that there are all kinds of families and they always have to be referenced.
The kids in my form (secondary) had all sorts of family situations. I would never assume or vocalise anything that suggested that all children have a family of mum and dad, both their natural parents, married to each other and all their siblings are full siblings. That was probably barely ever the case. It was fine. It really wasn't an issue. Teachers today in secondary and especially in primary bend over backwards to support DC whatever their situation.
Your child's class and certainly their school may well have kids with one parent (mum), with one parent (dad), with two dads, two mums, parents of different races, parents from different countries; kids will have a step parent, step siblings, half siblings. There will be families with all numbers of children, there will be DC who are adopted, who are twins and triplets, who have small age gaps to their siblings, who have massive age gaps. It's all fine. I honestly think you are massively overthinking this.
Wrt the worksheets, apologies if I misunderstood. I thought you were talking about a reception class – where most DC will not be able to read tbh. Yes, worksheets will be used further up the school. But tbh I don't think use of worksheets is a reason to jump to homeschool if it's not practicable (and it sounds as tho it isn't).
My advice would be to check out the likelihood of an offer from your preferred school; accept the school you are offered; go on waiting lists of any you prefer, if relevant; and consider an appeal but be aware that it will not be easy to win, based on what you have posted here, sorry.
Edit: ah if you were educated overseas that explains the bizarre situation of you being in all kinds of different classes etc. Pretty sure that would not happen in England.