It's so tempting to spoil him, but I know I can't right now since it is clear he disrespects me.
Depends what you mean by 'spoil'
If you mean give him whatever he wants, when he wants it, regardless of his behaviour, that's not a good move with any horse(or dog or kid...) regardless of their prior education. If you mean giving him whatever he wants whenever he is doing whatever acceptable, 'polite' behaviour, even if that is just standing around looking cute, that's fine. Just remember, horses learn from instant reinforcement & whatever behaviour he is giving you when you 'spoil' him is what will be reinforced/strengthened.
Also depends what you mean by 'respect/disrespect' as to whether he's doing that. If it's simply a lack of 'manners' or other behaviour you want him to do but he hasn't learned, I don't believe it has zip to do with 'respect' any more than a kid who's never been taught better eating with their mouth open or not saying please & thankyou. It is simply a matter of lack of education. For this & other reasons, I don't think it's helpful or very accurate to lable horses as 'disrespectful' generally.
You shouldn't be lunging a 2yo much at all anyway. And you need to teach him the basics & build up to doing stuff like lunging anyway. If he doesn't even know how to yield to direct pressure reliably yet, you've got a lot of 'kindergarten' stuff to do first.
The moment I take the pressure off him, he slows to a walk then stops.
Sounds like a good start. Get him reliably doing that when asked, and reinforce it, before beginning to ask him to sustain whatever gait for short times & gradually building up to whatever you're wanting. Baby steps.
he does not respect personal space. He shoves his head into me to look for treats
So just ensure that behaviour NEVER works for him. And you can also correct him - make him back up suddenly if he does it or otherwise punish him *when he's doing it, in order to make that behaviour have unpleasant consequences & he will soon stop. Particularly if you also 'spoil' him for alternate 'good manners' such as standing back & keeping his nose to himself.
and sometimes is stubborn on the lead rope.
I'm guessing you mean he either drags on the lead or hangs back. He just needs to be taught clearly how to yield to the pressure from the halter. If you're not sure how to go about those sorts of basics, you really need hands on help to learn how to teach him, as the 'blind leading the blind' will commonly go very wrong.
I want to show him I'm alpha without hurting him.
The 'alpha' or 'dominance theory' is actually from old behavioural studies of how wolf groups interact(faulty - not natural but from strange wolves thrown together in an enclosure). It is not really an accurate perception of wolf/dog relations, let alone horses. IMHO you'd be best forgetting it & just focussing on learning how to effectively train & learn to understand & communicate with your horse.