Is the baby oatmeal a lot smoother? Can you whizz up a batch of the ready oatmeal to make it a finer grain and then try that (I mean whizz it dry so if it works you can whizz up a big batch to keep in a food container and then make the individual serving the usual way in the mornings).
I see no harm in a 4yo still having a 'baby' cereal, it's probably healthier than most other cereals (not sure where you are but in the UK most cereals are not great, oatmeal or ready oats of course is fine if LO will eat it but here most cereal is sugary junk) and if it starts her day off well then why not. I expect it's fortified too so she's getting the added vits which can't be a bad thing.
I do totally understand your desire to move on though. My DS (4yo) has only recently moved on from his baby muesli!!
He would not eat porridge or instant oats even with honey mixed in, he politely said yum and then that he was full so I stuck with his baby stuff until around 4yo. It really is only the last few months we've been able to move on.
I found a muesli with no added sugar (well no cane sugar) and no big hunks of nuts but a mix of grains and 50% fruit. I discovered he would accept this so long as I soaked the muesli over night so it was nice and soft by the morning. It helped that the pack was pink, his fav colour, and there was a bit of discussion with him about grown up cereal and the cost of the baby stuff (about twice the price of the one we switched to and 4-6 times the price of other mueslies!).
He has since tried another mix which he couldn't cope with (lots of chunky nuts) and another which he also managed to get through a whole pack of before asking if he could switch back to the pink pack.
Hmm..I suppose I'm saying if she can't move on don't stress about it but also maybe worth trying a few other options to see how it goes.
Can you taste the baby oatmeal and see how sweet it is and the texture so you know what you are aiming for?