Teams points are for your team. Should you change team members, your most used team for the circuit will get exactly one fourth points for your other placements added to your total score. Your other teams cannot be considered for prize money and are effectively "disbanded". If you have a different teammate each time, your most recent teammate will be used.
This rewards consistent teammates, but doesn't punish you harshly if you have to have a random teammate.
For example, a player that gets first for 3 events (40 points) but changes teams every event would have 20 points to add to their final score of 40 at the champs for each event.
40 + 10 + 10 + 10 =70 points from that one player. Assuming his teammate got 3rd at each event prior, (5 + 5 + 5), they'd have 85 points total.
30 + 30 + 30 + 30 =120 (a team getting second each event)
As you can see, this does not allow you to team with a different person every event and make bank at the end. If you happen to team with someone random due to missing an event but got 1st with your teammate every other time, it would look like this:
10 + 40 + 40 + 40 = 130
Thus allowing you to miss a grand total of one event and beat a team that gets 2nd every time with consistent teammates!
To sum it all up for you without examples:
You may only receive prize money for one team at the end. The most played (or most recent if the teams all had the same number of events) will be used and that team is effectively disbanded and cannot be included in the rankings.
If you change teams mid-season, you will get 1/4th the points from your previous events added to the team being ranked.
All teams points are used for seeding for the championships.