There are no magic solutions!!
There is also a little bit of a paradox in your requirements - you don't have time for extensive workouts, but you want to improve your dancing.
Improving your dancing significantly will take lots of time and practice.
A high level of fitness (aerobic, strength and flexibility) is the only reliable platform from which to develop the specific skills and fitness requirements of the sport (plus, of course, improving your general health). Like any sport, dancing has its specific fitness requirements.
You can of course work on all the elements required - stand on one leg with your eyes closed and this will teach your brain to improve your balance - keep your leg muscles strong - do back extension exercises etc - but at the end of the day, there is no substitute for quality practise (under the guidance of good teacher) of the dancing you're interested in.
I used to have problems with my alignment and balance in the whisk and chassis movement in ballroom, so i developed a practice routine i could do at home on my own, and i did it for 20 minutes every day for many weeks. I have no problems now (not with whisk and chassis, anyway!!) This is the sort of work you will have to do if you want to seriously improve. It all takes time and a serious committment and there are no short cuts. If anyone else has good ideas - - please let us know!!