How the skills are determined is by looking at all three of your skill tabs. Any skill that you can put a point into at that time based on your level, prerequisite skills, and maxed skills, is assigned a number.
All of the skill tabs for every class, along with details of each skill, can be found on either
Arreat Summit or
purediablo.com.
As an example, a level 1 Barbarian has these skills available: Howl, Find Potion, Sword Mastery, Axe Mastery, Mace Mastery, and Bash. So if you get a Barbarian, you would assign a number to each of these skills, like this:
1-Howl
2-Find Potion
3-Sword Mastery
4-Axe Mastery
5-Mace Mastery
6-Bash
You don't necessarily have to have this order, but some way to differentiate them for random selection. Let's say you get Sword Mastery. You would then put your next three skill points into Sword Mastery. Your next skill selection would still have the same options, because no new skills will be available yet (you will only be level 3 or 4, depending on whether or not you've gotten the skill point from the Den of Evil quest yet or not), and nothing will have been maxed yet. So let's say that your next skill is Howl. You will put your next three points into Howl. Now at the next skill selection, you will be either level 6 or 7, so new skills will be available to you. These are now: Howl, Find Potion, Shout, Taunt, Sword Mastery, Axe Mastery, Mace Mastery, Polearm Mastery, Throwing Mastery, Spear Mastery, Bash, and Leap. You would then assign a number to each of these, in the same manner as before, and a skill would be randomly selected from these.
As for the weapon masteries, yes, you could in theory end up with 3 points in each mastery. However, that is why you have the 10 rerolls, to reduce the chances of something like that happening (unless you want it of course).
Also, with both you and your wife playing, make sure there is some way of distinguishing your two characters. The preferable way would be for you to each post separate, same as my wife(water_moon) and I are doing. It could in theory also work if you post both of your updates, and specify which is which, but the first way would be better.
I hope that answers everything, but if not, ask away, and I'll give what help I can. Or someone else (go AE :thumbsup: ) may pop in with the answer.