Learn English – What does ‘would that I had’ mean

This can mean either:

• Because of you, I will never be alone.

  This could be better re-written as "With you, I will never be alone."

• Whenever I am with you, other people will always be nearby; the two of us will never be alone together.

  Note that this does not indicate whether I want this to be the case. Compare two uses:

  I want to tell you a secret in private, but your parents are always watching us. I will never be alone with you.

  I know that if no one is watching, you will try to rob me. To protect myself, I will never be alone with you.

_{I am a little leery of offering no corroboration of my answer beyond the accident of my own birth, but several people have asked me today to post such answers, so here goes.}

It's a joke. Fundamentally it's approbation of your correct use of (what many people find to be) difficult homonyms.

First: You had me at is a jocular way of saying I was yours at the very moment you.. or You possessed my heart at the moment..

The original was You had me at "hello", meaning I was in love with you from the moment I met you or you didn't have to say anything more than "hello": I was immediately enchanted.

Here, the proper use of you're is a snarky reference to the fact that many (many!) people confuse the homonyms you're & your (i.e. use them improperly), so someone who used them correctly is a very rare, special, endearing, enchanting person indeed (to people who care about the proper use of English.