The longer I teach exercise, the more I appreciate old school, no bullshit technique. Joseph Pilates developed his mat exercises in the early 20th century as a simple body weight workout that can be done efficiently in a small space. I like basic bodyweight exercises such as jump squats, step ups, walking lunges, jumping jacks, squat thrusts/burpees, push ups, and all forms of planking.
Kettlebells are another favorite of mine. Used by Russian fish mongers in the 19th century, these give a huge amount of bang for the buck with core strength, weight training, flexibility, and cardio all in one workout. The TRX Suspension Trainer, originally developed by US Special Forces soldiers in Iraq and Afghanistan out of parachute cords and now sold to traveling business people, offers good simple bodyweight exercises similar to the old gymnastic rings.
If your trainer seems to be a member of the workout craze of the month club, you should worry. Are you constantly moving from the Bosu to Yogilates to P90X to Boot Camp to Pilates to Zumba to Super Slow to High Intensity Interval Training? Can your trainer explain why? Is your trainer even qualified to be teaching all of these things? If you have a hard time sitting and standing, you need to work on basic squats on the ground, not on an unstable Bosu. The Bosu may help you add stability once you are strong and steady on solid ground, but should not come before. If you came for Super Slow (although why is beyond me), you shouldn't suddenly be running Tabata intervals on the treadmill. Be smart and be safe!