Re: Question about been or being
"Been" is a form of the verb "to be" that is used with other verbs.
I have been.
I had been.
I will have been.
I'm sorry that I've been late to the last few meetings. The class I had right before hand is over now, so I'll be on time from now on.
Also, "Sorry for" requires a noun or noun-like thing.
I'm sorry for my lateness.
I'm sorry for the mistake.
I'm sorry for being late (being late is a gerund, a form of a verb that acts like a noun)
I'm sorry for missing the deadline.
You need an -ing form here.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.