Oh, my goodness. I'm so sorry.
The short answer is yes, it's going to be HARD. Any time you are connected to a destructive mental illness, let alone illness plus addiction, it's hard. And you and your kids are now connected. Luckily you don't have to deal with it directly, but in a sense you're at the whip end. Your stepkids will put you through it, and frankly the fact that they don't have more problems, and are this together, is testimony to your and your dh's parenting skills. But it will likely keep on being more of a problem than you'd get in a "normal" circumstance for years. No wonder they're clinging so hard to their old home. And I know your kids need more, but really, you can't tell kids in your steps' situation to suck things up. You can wish it, but -- how shall I put this -- they may already be at maximum suck, given their mom's behavior and problems.
The thing is there isn't really anything your kids can do about the vibes they get from their new sibs, and it isn't about them, which is a very tough thing to believe at 7. All they can really do is give their new sibs room. Which makes it even more important that they have their own space, really their own. You can't give someone room if you're already up against the wall.
If your dh's kids don't have a good, wise therapist, that'd be a start. But yes, basically, if you're together as a family, in some regards their mom's illness will have some effect on your kids, even though you and your DH will be a buffer. I'm guessing, though, that on balance the good outweighs the bad here.