If you follow your NUT/surgeon, which is probably the best right now, please make sure you tell them that you work out that much and make sure they know you are not just talking. Everyone says they "work out". You can work out and barely burn 150 calories walking at 2.5mph for 30 minutes. You can also work out lifting weights for an hour and then doing 30 minutes of intense cardio. Make sure your doctor knows what you do and adjusts your calories/meal plan accordingly.
You only consume around 400 calories, and your trainer is absolutely right to say that you cannot workout on this low calorie count. His recommendation is clearly not for a fresh sleeve, but you have to find a middle ground between the person who knows your medical history and the person who knows your activities. Cross check his recommendations with your NUT and you should be good. If you cannot eat that much, tell your trainer and ask for some foods with a higher calorie density - a slice of whole grain bread with Peanut Butter and some low sugar jelly can give you a good energy boost with 200 calories and should be easy to eat.
Don't try not to eat more - it may look counter productive, but it isn't. Even if you drive your car very fuel efficient - you MUST have fuel or you don't go anywhere or strand half way down. Just when working out, you don't strand but keep going and damage your engine.
As for Snacks, I too eat snacks. I was told 4 meals - ie. two meals, one snack, but I usually have two smallish snacks and at times, it looks more like I am having 5 meals with a little less than 200 calories for a total of 900 calories. In the end, the NUT gives you recommendations - you have to find what works for you.
Over the last 3 months since surgery, I have found that it doesn't matter too much when I eat, what I eat or how often I eat, what matters is my total calories and my workout. If I stall, I stall no matter what. If I lose again, it's just because my body is ready and not because I worked out more/less, ate more/less carbs/fat or so. I just came off a 23 day stall, and that after I ate everything "wrong" (like sushi, alcohol, snacks)