The core idea of this build seems to be: you want to have a high AC and be a tank, but you only need to spend two levels on paladin to pull that off, and you're going to spend the rest of your levels on something with higher utility. I haven't tried this myself, but I've seen others try it and it seems to work pretty well.
The thing where you heal yourself as a warlock seems like a good trick. It's only a tiny bit more healing than you would have gotten from Lay On Hands as a normal paladin, but having it be a bonus action is useful.
Smiting using your warlock spell slots is also a good trick.
You've written that you want to have a high damage output to draw aggro. I don't think this will work as well as you want, because being a multiclass character will drop your damage output significantly. In particular, a single-class paladin would get Extra Attack at fifth level, and you're not going to get that until much later.
You'll get shadow blade instead, but it's not as good: the damage output is less (2d8+DEX with your build, versus two attacks at 1d8+DEX each for the paladin), you're spending spell slots which could be used for other things (like smites), and every time you get hit, you'll have to make a constitution save or lose your weapon.
(Also, tanks don't hold aggro by having high damage output. Tanks hold aggro by having the Sentinel feat.)
As a side note, it's not surprising that it's hard to optimize both AC and damage simultaneously. If there were a build that gave you high damage and also high AC, everyone would be doing it already.
As Andras notes, your current build requires STR 13 and a high DEX. If you switch to a STR-focused build, then your stat requirements go down and your AC goes up, at the cost of some initiative. I'm not sure what your stat array looks like, but one guess might be that you'd go from 13/15/12/8/10/14 to 15/8/13/10/12/14, and you could put a racial +1 in CON to get bonus hit points.
I don't think Agonizing Blast is a good choice for you. Your eldritch blast spell has a low attack bonus because CHA isn't your primary stat; also, it will have disadvantage any time you use it while in melee combat. Warlock invocations are valuable, and it seems weird to spend one for a minor buff to an ability you'll rarely use.
I'm unsure about Grasp of Hadar. You might be able to use it to pull foes out of the air, or to pull them away from allies they were grappling. Those are good effects.
But the thing is: you're also spending an ASI on this (for War Caster). There are lots of super valuable things you could be doing with an ASI and two warlock invocations. The ASI could give you +1 to attack and damage rolls; the invocations could add non-combat utility to your character with Beast Speech or Mask of Many Faces or Misty Visions, or you could just get the Devil's Sight invocation and use the darkness spell.
