Hi KahlanA, welcome,
You made an excellent choice, Pekins are great, very tame, and they go broody easily so they can do the following years' hatches for you

I keep 4 pekins, plus about 20 other birds. I also use a Brinsea Mini (the Advance) and a bigger Brinsea (though the Mini is better) plus 2 ecoglows. I also use plastic coops.
With regards to the stable temperature, I have a different Mini but it probably means the ambient temperature - so not putting the incubator itself in a spot that is in sunlight behind glass or in a draught. Ours is in a heated spare bedroom. The first few days after the chicks have hatched I put the brooder inside a clear plastic box.
My pekins do quite alright with the bigger hens, except one of my bigger ones is quite the bully and thinks the pekins are an easy target - she might just be removed herself. They all live together in a huge fox and rat proof run in a field and use the same coop and nesting boxes. The pekins do have a sheltered area they can hide under should they wish or need to.
You could always buy some day olds of the more prolific layers on the day your pekins hatch, that way they'd grow up together. It wouldn't prevent bullying but at least you wouldn't have to introduce strangers with the upset in the pecking order that that brings.
I would be wary of mixing vaccinated with non-vaccinated birds. Ex-batts will have been vaccinated and carry all sorts of viruses they can cope with because of their vaccinations, but your pekins will not be vaccinated so they would suffer from the live vaccines and viruses the ex-batts (or any commercial vaccinated stock) would carry.
Plus most ex-batts are in poor health and have oodles of problems, their eggs aren't that good and not numerous and they don't live long at all - often just a few months after being rescued, though there is the odd exception. They're called 'spent' hens for a reason, unfortunately. But you do (or at least I do) get great pleasure out of seeing them enjoying life, and the basics such as sunlight, grass and dust bathing. For that alone, I find looking after ex-batts worth it.
Just a few tips: I love cats but they are a major problem where I live - they'd take my Polands and other bantams as soon as I turn my back. I added smaller sized mesh to the garden run (an Eglu) to stop the cats sticking their paws through like I've caught them doing (a children's watergun turned out to be very useful indeed). Crows will take chicks, btw, and foxes will come around in broad daylight even in suburbia.
We just hatched 6 cream legbars last night (another tip: put the eggs in at lunchtime so you can watch them hatch three weeks later during the day - if you put them in in the evening they'll hatch whilst the kids are in bed). We just returned from the field where we placed two of those chicks under a broody pekin and she took to them straight away. Pekins are such good broodies
Chances are in a few weeks' time you and your kids will be watching the chicken channel rather than ordinary tv!