The OP has: "Tom is half-brother to Peter by a former wife"
Purely hypothetically speaking (sine we already know the real answer), this means that Peter and Tom have the same dad, but different mothers (unless, of course, we're talking about one of the mothers being a lesbian ..., but never mind, that gets a bit too complicated). :-)
We're assuming that the dad is currently married to Peter's mom, which is the most likely explanation. However, if the dad was married, say, five times and his current wife is not Peter's mom, chances are, the sentence might be "Tom is half-brother to Peter by a former wife."
Here's a play (unfamiliar to me), which employs the above phrase:http://en.wikisource.org/wiki/The_Way_of_the_...
MIRA. What, is the chief of that noble family in town, Sir Wilfull Witwoud?
FAIN. He is expected to-day. Do you know him?
MIRA. I have seen him; he promises to be an extraordinary person. I think you have the honour to be related to him.
FAIN. Yes; he is half-brother to this Witwoud by a former wife, who was sister to my Lady Wishfort, my wife's mother. If you marry Millamant, you must call cousins too.
I, for one, have no clue what this actually means, i.e. which half-brother is the elder or what exactly the relations are here, but it seems to me, it could go either way.