First let’s give names to the tenses you’ve asked about, using the verb ‘to have’:
has had = present perfect
had = simple past
had had = past perfect
The simple past tense (2) is used to talk about things that were done (and finished) in the past. In spoken English, you will rarely hear the past perfect (3). The past perfect is used more often in written English. One way to use the past perfect is in a sentence where there are two finished actions, but one happened before the other. The past perfect tells you what happened first:
He had just left when they arrived. --> First he left and then they arrived.
In the sentence above, the order of events will change/be misunderstood if you do not use the past perfect:
- He just left when they arrived. --> First they arrived and then he simply left.
In prezbucky’s example, he began a story by saying the mother was tired (simple past tense). Then he described what happened before that (the things that caused the mother to be tired). In spoken English, prezbucky’s story would probably be told in the simple past tense, but the way prezbucky used the past perfect is common in written English.
There are some other “rules”, too. What I have written above is very basic.
As for the present perfect (1), I’ll come back to that later if no one else wants to take a (further) stab at it. But, I will say this: The present perfect is not used quite as often in North American English as it is in British English.
Why do you think the verb tense might be connected to a third person we don’t know?
‘Gotten’ is absolutely standard and 100% correct in American English. It is the past participle of ‘get’ and is exactly what the British used to use before they decided to make ‘got’ the past participle of ‘get’ (which was some time after they established colonies in North America).