The more I read from the OP, the clearer it is that, if her stepkids come to live with her, her dh and the other children (hers and theirs), her dh will not be independently motivating himself to do his fair share of the parenting - whether you think he should do all of the parenting for his children, or whether you think they should share the responsibility for parenting all the children.
The only way the OP is going to get him to step up and do even the bare minimum is for her to organise the jobs, tell him what he needs to do, and then make sure he does it - and that is just leaving her with the mental load of all of it.
Even the uniform and packed lunches issue demonstrates this. Her dh should be making sure his children's uniforms are washed and ready to wear on Monday, and doing their packed lunches, but it is pretty clear that the only way that will happen is if @ahhhhhhhhhhhhhhhhhhhhh takes on the mental load of supervising him doing it all.
I feel sorry for the children - and there is a part of me that thinks that, if her dh isn't stepping up, and the kids are regularly going to school in unwashed uniforms and without packed lunches or lunch money, it would be the kind and caring thing for her to step in - either wash the uniforms herself on Friday night, so they are dry and ready on Monday morning, or nag her dh to do it - and the same goes for the lunches. But equally, I can see that, if she did start doing this, even whilst they are only there every other weekend, she would end up doing it full stop - her dh wouldn't start being a better dad - he'd just happily abdicate the responsibility to her.
I can't see a good answer to any of this. The only thing the OP can do is to sit her useless dh down and have a come-to-Jesus talk with him, setting out all the things that a parent has to be responsible for, telling him that he is already failing to do the bare minimum of that for his children, every other weekend, and then to ask him how he plans to parent his children - with all the extra responsibilities that entails - without just assuming that the OP will do all the extra work.
If his response to this is positive, and he accepts he needs to up his parenting game massively - and if he agrees to a trial period, during which time he must show that he has actually learned the lesson, and made the changes, then maybe she could consider the new arrangement - but frankly I am not optimistic that he is capable of it.