"You're not the boss of me" emphasizes "me," and is something a child would say (or we imagine would say) to his parents. It's also often said by an adult to give the statement that connotation, sometimes in an ironic way.
"You're not my boss" is a bit more on-the-nose and declarative, whereas "you're not the boss of me" is more absolute, confrontational, and draws more upon the cultural shared knowledge of that phrase.
Interesting question! I don't think a single English word exists for this, at least not one that would be readily understood without explanation. If you want one, you'll have to make it up yourself, and be prepared to explain it. Antiversary, for instance, seems cute and compact, but is readily misinterpretable (a friend suggested to me the other day that an antiversary means one year after a couple breaks up).
But if you're willing to use more than one word, negative-first anniversary seems readily understandable; if I'm going to get married a year from now, it's my negative-first anniversary. Googling "negative one anniversary", "negative anniversary" and so on turns up plenty of hits, suggesting that this is a natural, intuitive way to describe the concept.
More colloquially, I often hear people using T-minus terminology - deriving from the countdowns we've all seen in movies, where rocket scientists say something like "T-minus 5 minutes" to mark the time until launch - when describing an anticipated event. So, for instance, a party that's held 1 year before your college graduation could be your "T-minus 1 year grad party."
Best Answer
Anniversary just means a marking of some number of years - not necessarily of a marriage. So provided there is an agreed start date to when the relationship came into being or reached some critical level ("living together", perhaps), you can simply celebrate the anniversary of that date.