Did Christ have the freedom to choose to avoid crucifixion? Inspired by this answer, Jesus talks about this authority in John 10:18 (NIV):


  No one takes it from me, but I lay it down of my own accord. I have authority to lay it down and authority to take it up again. This command I received from my Father.”


In precisely what sense does Jesus have this "authority?"  @Richard's answer (linked above), suggests that this means Christ had the authority to either lay down his life or not...  But that's not the only way we use the phrase "authority."

Consider a police officer with a warrant to arrest a suspect.  He knocks on the door and says "I have the authority to arrest you."  This doesn't imply that the officer has a choice in the matter.  He does have the authority to make the arrest, but he also has the obligation to make the arrest.  A failure to make the arrest (except for extenuating circumstances) would result in disciplinary action against the officer.

Did Christ really have "free will" in this matter?

In fact, Christ even says it's a command from His Father; which suggests that he did not have authority not to give up his life.
Yes.

Jesus' own words to Peter are relevant here:


  Matthew 26:52-54 (ESV)
   52 Then Jesus said to him, "Put your sword back into its place. For all who take the sword will perish by the sword. 53  Do you think that I cannot appeal to my Father, and he will at once send me more than twelve legions of angels? 54  But how then should the Scriptures be fulfilled, that it must be so?"   


The way I read it, Jesus genuinely had a choice to call out an army of angels that would have been enough for world domination.