You've got the right idea to get stronger for tennis.
But you're going in the wrong direction if your goal is to get your hips to split wider open.
What you really want is some simple exercises that will exercise the leg muscles, the core, and the muscles that connect the muscles to the core.
Notice that in every serve, good servers do an exercise called the squat.
Notice in the photos above that Sampras squats down, then pushes powerfully up.
So you should be doing the "king of exercises" - the squat.
The above images show someone squatting with barbells, but you can start with squats just using your own body weight:
Doing this simple exercise will allow you to let your body weight sink down while remaining balanced, just like Sampras does in his serve above.
As you become more experienced you can add in some dumbbells to get even stronger.
(If you want to, you can even join a gym and get instruction to learn to squat with barbells.)
You can even learn to jump out of squat, to better duplicate the dynamic move that should help power every serve:
Squat Drop Jump http://www.xlathlete.com/view_exerci...ercise_id=1330
(Don't do these too early, or you will be risking injury.
The other exercise that is very good for tennis players is the lunge:
Again, start with just body weight lunges (no dumbbells) and you can add the dumbbells in later.
Adding in an upper body twist also is a great variation to work your core more:
Lunge With Twist http://www.xlathlete.com/view_exerci...ercise_id=1585
If you just squat and do lunges I think you will get the results you are looking for.
[You will find that the whole body is used in the kinetic chain. So if you are interested in training further, consider the following:
The Elite Approach to Tennis Strength Training http://www.sport-fitness-advisor.com...-training.html
And don't forget "running" as defined by this USTA coach:
" When training the players the USTA works with, we usually do some sort of "running" four to five times a week. The running session usually lasts between 20 – 40 minutes, but there is a lot of variety in the types of running we do.
You’ll note that we put running in quotation marks, because much of what we do is different from the long, slow distance running many tennis players are familiar with – there is some long distance running, but the “running” sessions also involve footwork/tennis agility work, or interval runs. The type of running depends upon the periodized strength and conditioning schedule of the player.
Generally, the long distance running and longer interval repeats (400s and 800s) are done during the preparation phase when you are getting ready for the season. Shorter, higher intensity intervals (20s, 40s, 60s, 100s, 200s, and 400s) and on-court footwork/tennis agility are the main focus during the pre-competition phase in the weeks leading up to main competition or competitions. During the competition phase of the season, on-court footwork/tennis agility is the “running” focus.
Recognizing that each player is an individual, we adjust the plan depending upon the player’s cardiovascular endurance, agility and their physical and physiological strengths and weaknesses."