I want to incorporate a vigorous workout routine into my daily schedule. I work about 10 hours a day (from 9:00AM – 7:00PM); and my commute to work/from work takes about an hour and 15 minutes. I usually wake up around 6:30AM to get ready for work, and get back home around 8:15PM or so. Since getting in a good workout doesn’t seem feasible before/after work (when I get home, I like to have dinner and relax until I turn in around 10:30 or 11:00PM), I want to develop a good exercise routine when I’m at work.
My charge usually naps for 1 – 3 hours two or three times a day. Since I don’t have to attend to any duties outside of childcare, this period gives me an ample amount of time to exercise. I’d like to work on my legs (thin out and tone my thighs, quads, and calves), core (lose some midsection weight and begin to develop visible abs

), and arms (particularly lose weight in my upper arms, tone and build muscle), and of course tighten my buttocks.
Overall, I want to lose anywhere from 15 – 20 lbs while toning my entire body to achieve a healthier self. I’m hoping to do so by May, because I like wearing shorts and tank tops when it gets warm/hot outside, and I don’t want to feel self-conscious about my body when wearing this kind of attire
MB and DB have Verizon Fios, so I have the option of watching numerous interactive fitness classes on demand. The variety is great (cardio, yoga, core, arms, etc.), and each program lasts anywhere from 20 min. – 1.5 hours. I actually tried a couple of workouts today. Truth be told, I sucked at keeping up with the instructor, and I entirely lack all manner of equipment.
Anyway, I plan on purchasing some dumbbells (perhaps 8 lbs), and a medicine ball. I’d like some advice from other nannies, SAHMs, and, WAHMs who have a situation similar to mine on how I should approach this. What other equipment should I purchase? Should I focus on one area of my body each day (e.g. arms on Monday, core Tuesday, legs Wednesday, etc.), or work to some degree on each part of my body each day? Approximately how long should I workout? Should I only workout once a day (say for 45 min. – 1.5 hours), or twice a day (for an additional 45 min. – 1.5 hours each)?
I’d also like to hear what kind of foods I should really start eating (i.e. fruits, veggies, any special smoothies/protein drinks, etc.). What should I eat before/after a workout. I’m a vegetarian, so no meat, eggs, or milk please (because I plain don’t like that stuff

)
I’d greatly appreciate getting some feedback from you guys so I can really get started by tomorrow. TIA