Usually we would say I do something during the day. If we use in the daytime, we are making it clear that it happens in the day, not at nighttime or in the evening

I do it during the day I do it in the daytime All the same

There's nothing wrong with the way you said it, except it's a bit vague. If this is your intention, that's fine. To elaborate: it's unclear whether you mean every day, or most days, or few days, or mainly today, etc. If you were a native speaker I would assume you mean generally some days, probably near the middle of the day - not too early in the morning and not too late in the evening. But the statement remains vague, so this is mostly guesswork.

Good question. Native speakers usually just say “during the day.” For example, “I work during the day” or “I usually exercise during the day.” The phrase “in the daytime” is correct, but it sounds a little less common or more formal. You might hear it in writing or careful speech, but in everyday conversation “during the day” is what people usually say.

Interesting question. So there are no nuances in using one or the other?