1. How to motivate yourself after completing an important competition?
Naturally after putting all of your energy into getting ready for championship, you will be depleted of the "drive." Now what? You want to make sure you have your practice schedule, coaches are staying consistent and you don't take a break. Remember every day you don't practice, you don't perfect your skill and stamina. Set your eyes on the next event and immediately start preparing for it. This is the best way to motivate yourself.
2. How to practice without a fight...
This is a million dollar question! Every couple is trying to solve this puzzle. What I am about to offer is just a suggestion, a tool which hopefully will help practice to go smoothly. You would need to create a structure for practice and some rules/guidelines (and if they aren't being followed - repercussions).
Turn the music on and first round of your dances should be half time; by yourself - all dances, basic steps and no stopping, no talking to each other (that includes no making faces, no instructing, not pulling your hand away, etc). Second round should also be half time, no talking, but together. Third round should still be basics, but full tempo. This one is still no talking. Fourth round is for the practice of your competitive dance routine. Again, no stopping, no talking, just full tempo and quiet.
So now you have done 4 rounds, in about 45 minutes and you haven't had the chance to argue. By this time, you've warmed up, tuned up with each other and too tired to argue (just kidding), but definitely now ready to work on parts of choreography which didn't feel good.
3. What else can I do to improve my dancing?
There are number of things you can do to help improve your stamina - running, biking, kick boxing. As well as to improve your elasticity and core - yoga, ballet, and even pole dancing. Any of those extra curricular activities will help improve your dancing.
4. How to pick a competition to attend?
There are at least two or three competitions each weekend in the United States. Picking the right ones can be expensive (geographically) and not successful in terms of exposure. If you are trying to get as much exposure as you can, you should plan to do rising star as well as open competition. Also see which competitions are geographically closer to your city. Once in a while you should try to go to a different coast to begin being seen by another crowd.
Remember the more people and judges see you, the more they will remember you the next time and will see your improvement. Also it will help that in the beginning of the year you will plan all competitions you plan to go to. That will help you stay motivated and don't take unnecessary breaks.