OH does care about my feelings
how's that then? Because from where I'm sitting, it looks as if he's completely disrespecting you as well as not giving a shit that you're being made miserable and is also happy to see you skivvy for him. So, lazy, using, manipulative and doesn't respect you at all. Care? Not so much, actually
but I feel on this occasion I'm on my own with it.
In other words, this is the first time something is an issue, so the first time you're seeing a glimpse of how he walks the walk (rather than talks the lovey dovey talk - which I imagine there's a lot of as he knows full well he needs to keep that coming if he's to keep his feet under your table and keep you skivvying for his kids so he doesn't have to!)
Anyway, it's not just you being 'on your own' with this - from your very short post, it's clear that there's also an issue with him letting his kids do what they like which is already having a detrimental effect on your parenting. And all the other stuff you allude to. You're 'on your own' with it all - because in short, he's not a keeper.
He's a cocklodger - and a particularly turbo-charged one as he's got kids who live with him full time, so it's not just a case of him needing somewhere to sponge services from for himself, he's got kids who need a skivvy and a substitute parent too (because as you can now see, he's not just physically lazy and won't lift a finger, he's also mentally lazy and doesn't want to set boundaries, offer support, set and example or ANY of the other stuff which means him lifting a finger.
He is a user.
You've already had the talks. But frankly, if he was a good man, a good parent, and a person who is going to make the good stepfather your children deserve, you would never have had to have the talks. It's your fucking HOME he's moved into fgs, if he can't even have the barest respect for that within what you say is a short time and he is already showing what a lazy using fuck he actually is, JUST GET RID.
He's going to have a negative effect on your entire life - your parenting, your children's example of the adults around them, your finances, your energy which he's already helping himself to.
Respect for him and therefore the 'love' that you are currently clinging on to will soon be gone.
There's nothing so persuasive as a cocklodger who needs to find lodgings and a skivvy for the kids he doesn't want to parent as well as himself, so please cut what could easily be a year or more of whining and pushing his luck and tell the using feck to get the hell out.