Your confusion comes from the fact that "home" can be used as either a noun or an adverb.
"Home" used as an adverb (merriam-webster entry 2 sense 1) doesn't need any qualifiers or prepositions. It means means "to my/our/your home." You would use it as follows:
"I'm going home tomorrow" (home = to my home)
"Are you coming home tomorrow?" (home = to our home)
"Go home." (home = to your home)
"Home" used as a noun (merriam-webster entry 1 sense 1) requires a preposition and additional adjectives/articles.
"Can I come to your home tomorrow?"
"I'm going to Sarah's home on Tuesday."
Regardless, if you're asking a question, you would need to switch the first two words of your sentence: "Could I" not "I could".