Can I get out the navy early to be with my wife and kid?

No, you cannot obtain an early release by simply being lonely.

A hardship release generally involves grave illness of a spouse or dependent family member. You do not have a chance at that.

You can only get out early through adverse action, which means you must intentionally screw up somehow and likely lose all benefits of your service AND have to deal with the sort of Discharge that makes it hard to find a job.

Your best alternative is to serve out your enlistment and move on with life from there.

I have every confidence you will make the wrong choice.

Why are they not with you? Unless you have unaccompanied orders there is no reason why they should not be. Just because they miss you and you miss them, isn't a valid reason to get out. Remember it is NOT how much time you spend together but HOW you spend the time.

Not without doing something that will get you kicked out.

While I understand where you're coming from, missing your loved ones and vice versa is not exactly exclusive to you sir.

There is something called a hardship discharge. You may apply for it. Seek info about it.