Should I challenge my teammates to be on my 1st singles team in tennis at my school?

If you think you're the best play the best. Simple as that

I'm wondering if the coach decided to put a relatively stronger player on *both* the 1st and 2nd doubles teams in order to try and win a point at both slots. Is the coach likely to split either or these two doubles teams apart? If not, then you're probably wasting your time thinking this way. If none of the four players involved here are good enough to play singles on this team, I would say, don't get too worked up about which doubles team you're on. Now, if you reckon that you and your current partner could defeat the #1 doubles team in a DOUBLES match, that might be worth asking for a challenge. The whole line of thinking too much about the ladder might be counterproductive for you. How about thinking about things YOU can do on [setting daily goals] your own to improve *your* playing skill. Can you work on your serve before school early in the morning? Can you ask another player to go and play, practice, or just hit some outside of regular practice? Are you able to use a ball machine at the local club or somewhere else? If things get dull and the coach isn't watching, you can work on hitting the ball behind your back, between the legs, catching the ball on your strings, catching a pop-up [high lob] on your strings, "fun stuff" like that. Again, I'd say just put up with the ladder, ENCOURAGE the partner that you're with [that's important], and think about things you can do to build up your skill level, whether it's: all the different kinds of serves [slice, twist, flat, variations of these], return of serve ["batting practice"] where you just to serve & return and nothing else groundstrokes, punch-volleys, overheads, drop shots, dinks, lobs, approach shots, consistency drills, etc etc etc