I'm a little late to this convo but I'll add a few thoughts.
Hopefully by now your trainer has given you a new way to look at how/when/why/what you eat. The biggest part is the application of that knowledge. He can tell you everything, but you have to incorporate it. Easier said than done most of the time, but it's really about making a decision. I think you should be successful with it since you've taken the initiative to get a trainer. Baby steps.
Working out versus running for fitness. If you like to run, by all means do it, but it does have its consequences. Steady state cardio is catabolic to your system. Lifting weights is anabolic to your system. If you do both consistently in the same training, catabolic wins every time. You won't show me a 1/2 marathoner or full marathon runner that has muscle tone...the running eats their muscle for energy. The best way to lose fat is to build muscle...the more muscle you have the higher your metabolism is, the higher metabolism is the more calories you burn just sitting around. Running works for those just starting out, but after a while you plateau because you're not as winded from the same workout you did last week.
I recommend full body workouts for those looking to lose fat and just get fit. Also High Intensity Interval Training is awesome for fat loss. A 15 min HIIT session will burn more calories than running 5 miles.
A simple version of a HIIT would be to do a basic weightlifting workout, but in between sets, instead of sitting there, jump rope/high knees/box jumps or something like that for 30-40 secs, then do your next set. This way by the end of your workout you will have done 20-30 min of cardio and not spent any extra time in the gym.
Another method is called PHA training. A sample of it would be:
These exercises would collectively comprise one cycle, with 4-5 cycles generally being performed.
Clean & Military Press 10 reps
Squat 10 reps
Weighted Pullups 10 reps
One-Arm Dumbbell Swing 10 reps
Standing Calf Raise 10 reps
Sit-Ups 10 reps
Do this program 3 times a week and avoid doing cardio in the off days.A proper warm up should be performed before starting the program.Do a week off after 6-8 weeks.