Can I use Decoy Dragon's effect after Dream Sprite's effect?
In short, Decoy Dragon would be attacked, due to an important part of Dreamsprite:


  When attacked by your opponent's monster, select another 1 of your Monster Cards and designate it as the attack's target, then calculate damage.


This means that damage calculation must be immediately performed, so the Battle Step has been skipped. As Decoy Dragon's effect is activated "when this card is selected as an attack target by your opponent's monster", it is only performed on the Battle Step (as that is when it is targeted), so is not activated in this case. An official ruling also backs this statement up:


  "Decoy Dragon's" effect is activated during the Battle Step when it is selected as the target for your opponent's attacking monster.


To back this up further Konami has also ruled the following two things about Dreamsprite:


  If you control "Dreamsprite", "The Legendary Fisherman", and "Umi" is on the field, "Dreamsprite"’s effect can still change an attack target to "The Legendary Fisherman" because he is not being targeted with an attack, but is being targeted with a monster effect.


This means that Decoy Dragon would NOT be being targeted by the opponent's monster, but by Dreamsprite's effect.


  If you control two "Dreamsprites" and one is attacked, you cannot continue to switch the attack target between the two "Dreamsprites" because the effect of "Dreamsprite" says that you must calculate damage on the new target.


This further emphasises the point that the Battle Step is ended due to the effect.

I hope this helps!

Source: Konami's Individual Card Rulings (web archive version as it has not been online since early 2013): http://web.archive.org/web/20090218205242/http://entertainment.upperdeck.com/yugioh/en/gameplay/faqs/cardfaqs/default.aspx?first=D&amp;last=E