Well whatever you want to do with the trigger.
Add the \b (boundary) such that it matches on
!dedi !dedicate and !dedication since without
the \b it was gonna match on !dedication anyway
and anything that followed !dedi command.
You could rearrange the whole if !$2 || !$3
to be as follows. No need for %whom just use $2
Only the first hadd needs the -m and %dedi
can be used for the whole hash table name one
time like below.

[size=17]You may want to add flood protection.[/size]

on $*:text:/^[!@]dedi(cate|cation)?\b/Si:#: {
  if ($3) && ($2 ison #) {
    if ($left($1,1) == !) .notice $nick $logo(Dedication) $c2(Dedication sent to $2 $+ !)
    var %dedi $+(durl.,$right($ticks,5))
    hadd -m %dedi whom $2
    hadd %dedi from $nick
    hadd %dedi info $replace($3-,$chr(32),+)
    hadd %dedi send $iif($left($1,1) == @,.msg #,.notice $2)
    hadd %dedi ornot $iif($left($1,1) == @,to1 $2,to you!))
    sockopen %dedi www.youtube.com 80
  }
  else { .notice $nick $logo(Error) Please specify a song/nick $chr(124) !dedication <nick> <song> <artist> }
}