“Sorry, I've kind of been in my own little world lately.”

Your wife is angry at you because you aren't paying enough attention to her. You're always focused on work and don't spend time with her. You want to apologize for not paying attention to her. You say:

Sorry, I've kind of been in my own little world lately.

kind of

This phrase means "a little bit". It's similar in meaning to "somewhat" but is more casual. Use "kind of" for most situations and "somewhat" when discussing academic topics or in writing.

I've been (adjective) lately

This is a way to describe how you've acted for a few days or months that's different from how you were in the past. When you describe yourself in this way, it sounds like this is a characteristic that isn't usual for you.

You can use a simple adjective like "tired":

I've been pretty tired lately.

Or you can use a longer phrase like in the example at top: "in my own little world". The phrase you use should be similar to an adjective, meaning that it should describe the noun ("I" in this case).

There's a little confusion about the difference between "recently" and "lately". "Lately" is more appropriate for continuing situations, while "recently" is better for events that happened just once, a couple of times, or that have continued but are finished now:

Have you been going to the gym a lot lately? You look great!

I ran into Stacy recently at the Food Emporium.

be in (one's) own world

This means to be focused only on your own thoughts, and to not pay attention to other people or events. This phrase is a metaphor. It's comparing your thoughts to being on a planet with no other people.

You can add "little" to this phrase to make the thoughts you're having "in your own world" sound unimportant and selfish.