You need to work very hard towards being liked, in this situation. Because as a step mum you can very easily be rejected, as you know. Not because of the person you are, but because of the simple fact of; you being the step mum.
You've carried on with using the same level of discipline as his mother did with him? But you will not love him as much as his mother did. If you're giving him the same harshness as a parent would, but can't give him the same intense love as a parent would, then it's going to feel unbalanced.
He's said you're not part of his family. Well maybe you're not considered as so right not, by him, at least his honest feelings are out. It may be a few more years, untill you're accepted fully. But I'm sure it will happen as he matures.
The best thing you can do right now is have an adult/child friend relationship.
I do this with my younger sister who's been in my care for considerable periods in the past, she listens to me, knows to do as I say when she needs to. But you have to be so tactful and thoughtful, because at the end of the day they can think 'you're not my mum, you have no right' and feel that it's unfair. They want their mum for gods sakes, it's a traumatic time, they're thinking this ain't natural.
You have to be a friend to them, and earn their trust, before you can be let into their hearts and respected as someone who can guide them and play that role.
You have to be more careful about what you say, saying his good points more. Listing his bad points in this post of yours saying he's lazy, uncooperative, an idiot- but I love him. I think that's a confusing message, if he were to hear you say that stuff. Because anyone can be suspicious of the words 'I love you' it's demonstating it which will allow it to sink it.
Maybe you having a chat wouldn't be so helpful as you might think.
But just changing the way you are, stepping back a bit. Focusing on his good points, arranging fun things, etc and not trying to dicipline him as a natural parent just yet, might help.
BTW I think what you're going through is normal, given the tough situation.