First one is used when the person being spoken to (the your) is female. The second is for the gender being male. Mike is a male, therefore it is بَيْتَكَ. However, as an Arab, I would be more likely to say بَيْتُكَ. I don't know the grammar rules, but it seems Jackass318788 agrees with me.
What you are saying seems to be consistent with Egyptian Arabic nowadays, but it isn't how they do it in the standard literary language. In fact, what you would say yourself appears to be (The script is so darn tiny!) the fusHa way. :-)
So baytuka is not standard Arabic but spoken Arabic? Baytek would be standard Arabic?
ki when speaking to a female, ka when speaking to a male. But why it should be "بَيْتُك" and not "بَيْتِك" or "بَيْتَك" is because it's a nominative case. Because we started the sentence with the it. In the accusative case like if it were an object, it would be "بَيْتَك". And in the genitive case like after a preposition, it would be "بَيْتِك". And That's the standard Arabic. In the spoken Egyptian dialect we would say "baitak" if the addressee were a male and "baitik" if the addressee were a female regardless of the case (bait pronounced like maid).