You should always demand respect on both sides of the fence.  The new parent shouldn’t automatically feel they will be respected, after all your child is watching them.  If they don’t offer respect, you can’t expect your child to return the respect without hesitation.  It’s just not the way it will work, and it is going to be a bit of effort if you want this blended family to thrive.  And it won’t just be you, but all of you that will have to put the work in for success.