I wasn't Marine but I was an Army Infantryman up until 2013. Personally I don't think your trainer is to cut out to really be helping you at this point at least with your goals. Boot camp us a ton of running not at a blistering pace 7 minute miles to even 8:30 of very long runs, ruck marches in foot battle rattle with 40-60lbs pack, and lots of pull ups, push ups and sit-ups . Also the occasional smoke session with burpees, rifle presses, or god only knows what else.
I don't know how long you have to get ready but I'll assume atleast 4 months. Id schedule my training something along these lines. I AM COMPLETELY GUESSING AS TO YOUR CUTTENT LEVEL OF PHYSICAL ABILITY.
Monday- Long Run w/ Moderate Speed start at 2 miles shoot for sub 8 mins do not kill your self but just sub 8 mins. Finish with 2-3 sets of push ups, sit ups and pull ups. Don't go to fail just shy of. Each week add 1/4-1/2 mile to the distance. May not seem like much but at the end of 4 months thats a possible 10 mile run. Plenty long for boot.
Tuesday: Upper Body Strength
Basic Barbell Movements. Bench Press, OHP, Pull Ups and Rows. Remember your not a powerlifter and being a body builder will not help you get any extra points. Focus on good tech 3-5 sets of 5-10 reps. Simple linear progression pushing for just a little more weight or an extra rep at each session.
I prefer running quarters here. Sprint quarter miles as fast as you can keep rest lower than an minute. Start with about 4-6 sprints AFTER A GOOD HALF MILE TO MILE JOG or so to warm up. When your good enough to get all 4 sets at under 90 seconds and your rest below the minute mark add a set and continue I wouldn't do more than 12 sets total. That's 3 miles plus warmup at a 6 minute mile pace. Finish with the same situp, push up, pull ups circuit from Monday. Cool down with lunges.
Thursday- off or very slow moderate run and stretching. You don't get days off in boot so take advantage of the recovery days now. Finish with stretching.
Friday- Upper Body Endurance Day. Focus on dips, pull ups, rope climbs, and the such. Keep reps higher and rest lower here then on strength day.
Saturday- Ruck March and Legs.
Ruck March with a 20lbs pack. Start at 3-4 miles and add 1/2-1 mile and 5lbs each week up to a max of 12 miles and a 70lbs pack. Once you get maxed out I liked to rotate each week.
Week 1- 4 mile ruck march with 35lbs pack tried for 10 minute mile or a very slow jog almost. A lot say don't run with a ruck but, I enjoyed it and the fastest of the fast and best ruckers I knew did them often. But don't be an idiot work up to it.
Week 2- 8 mile ruck 55lbs pack tried yo hit a easy 13-14 min mark this is easiest week.
Week 3- 12 mile ruck 75-85lbs and just do it. If you can't keep atleast a 15 mile pace you need yo lighten the load.
After the ruck we always squat, pushed sled, and did GHRs. May take a while to work up to it but, worked great for me.
Sundays- I suggest taking this day off especially once you get to a much heavier and longer rucks. But if you insist a very slow recovery run and stretching.
Like o said don't know your level of experience so I am being very general and just trying to help give an idea that worked for me.