"I wonder how my life would have been different had she lived"
- There is no IF because she is using a different grammatical form, where you use "Had [subject] [past tense]" to indicate a past alternative that would have led to a different present. Like, "Had I known things would turn out this way I never would have invented that time machine". It's equivalent to the "IF" form but it's less common and a bit more formal. Maybe with more connotations of regret ?
Here is a video talking about several inversion forms including this one (at around 4:00)
http://www.engvid.com/english-grammar-inversion/
- It is implied she is talking about her life up to that point. "Childhood" wouldn't work because presumably her whole life would have been different, not just her childhood.
Grammar
I wonder how my life would have been different had she lived.
In English, conditional adjuncts look like interrogative clauses. We can use if-clauses, which look like subordinate closed interrogative clauses as conditional adjuncts:
- If Bob won, he won by a large margin.
- I wonder if Bob won.
A different way of doing this, is to use clauses displaying subject-auxiliary inversion. These clauses look like main clause closed interrogative clauses:
- Had he won, he would have won by a large margin.
- Had he won?
Here we see the subject and auxiliary verb inverted. We do not use if to mark the conditional adjunct if we have marked it with subject-auxiliary inversion. This is in the same way that we do not mark interrogative clauses with if when we have already marked them using inversion.
Meaning
We are often told that conditionals using past perfect forms ("third conditionals") refer to past time. In real life this is not the case. We often, in fact, see past perfect forms in conditionals referring to the future:
- If David Beckham had been playing tomorrow, we would have won.
We often use this kind of conditional to refer to a situation whose outcome has already been fixed in some way, regardless of whether it is going to happen or already has.