Sorry I don't think you're being unreasonable at all.
I think there is no place what so ever for a job share in rec. The only people it suits are the teachers themselves. I know life happens but I actually think job shares should only be allowed from KS2 up. Primary teachers should be able to teach across the age range so it shouldn't be a problem for teachers to cope with that.
I am an ex teacher with a lot of experience in rec and KS1.
I'm surprised your head has put a job share in rec as most wouldn't dream of it certainly in all the schools I've ever taught in.
Rec is an extremely important year and children need a huge amount of continuity and security. This is seriously limited with a job share. This is a child's 1st taste of school and it will take a lot for a child to cope with being in the full time care of a new adult let alone cope with learning to read and write and everything else school throws at you.
For a 4 year old to have to cope with a different adult,different teaching style half way through the week is just not on. It will just make the delicate procedure or teaching that child the very important basic skills that much harder. Learning to read and write needs to be handled very carefully you really need to build a child's trust and confidence. Not all children are super confident certainly not at 4. Also both will have PPA time and an assistant so frequently it isn't actually just 2 teachers involved.
I also think it takes an outstanding set of teachers to compensate for being a job share,how many of those are actually around? I've taught as a job share on supply and it was a nightmare trying to do the job as it should be if the other half has a life and sticks to contracted hours. Done properly there should be a hand over period every week(would take an afternoon if done properly),planning,assessment etc,etc.I was constantly chasing said other half who quite rightly didn't want to go over her paid time to discuss important issues that actually needed to be discussed.
I have several friends who teach as job shares and interestingly most like me don't think they have a place with young children at all. Older KS 2 children have learnt the basics, are settled into school and are a lot more confident,far better able to cope with the demands of a jobshare.
Complain big time,even if you don't get a result this year your head might think twice next year,could benefit you in the long run if you have other children.