As far as potty-training goes and it's relationship to development, it is my opinion that most late-potty-training has nothing to do with a child's development whatsoever. It's simply indicates the age that the parent got serious about potty-training!
It's at least a week of nasty wet everywhere, and so most parents get faint-hearted, understandably, and quit halfway through, thinking mistakenly that "it isn't working," when in fact, it's working just fine. It's just take a little
time for a child, that WE
TRAINED TO PEE IN HIS PANTS (heehee!), to learn to go to the bathroom in an entirely different location.
My troops are all trained right before or right when they hit age 2, simply because a wiser older mother clued me into the fact that it's simply a matter of adjusting habits, having nothing to do with anything 'deeper.' And so, of course I make it fun and exciting (and give reward the first couple days, and buy new 'big girl/big boy' pants for the new little big boy/girl, but...it's not a matter of whether they want to or not. It's simply a matter of diapers no longer existing!
I think when parents wait till the child is 3 or 4, the child then feels an emotional attachment to his/her diaper, and also doesn't like change, and also realizes he/she has a bit of pull in the situation--"I don't want to." If you get them
before they hit the preschool stage, they don't even realize they have a decision!

They just figure "Hey, Mom said we're out of diapers and besides, we don't wear them anymore: I get to wear these cool cloth underwears now... and by golly, they sure get itchy when I urinate in them!"
That, of course, is only my opinion, nothing more! *grin*
But as for your 2 year old, sounds like a 2 year old to me!
The most important things to teach a 2 year old is that they are SAFE, LOVED, and ENJOYED. They also need to learn simple obedience (to obey simple commands right away), and how to work.
Lots of work done side-by-side with Momma (like folding washcloths, etc...) forms great work habits into them, which
later translate into good educational work habits too!

Work times with mom serve as a great time for singing Bible memory songs and talking about important things like, say, "Boy, I just love that Daddy! He is such a good Daddy, isn't he? And did you know that Daddy loves God? He obeys God too!" or, perhaps, "Aren't we so glad that we have Jesus to take care of us? He is just so good!" The time working together also teaches them that
mom loves them, likes to be around them, and needs their help. For a 2 year old, life doesn't get much better than that!
Love,
Molly