Dunninla hit the nail on the head with the traveling part and the individual sport aspect of training. Running and swimming are a lot alike in that aspect.
I still did PT in the mornings, and at one point started earlier on days that I had to lead PT. This coincided well since my training regiment for running was 2 a days. It got the point where I would shower in the gym immediately after and carry my PT gear around most of the day so I wouldn't waste time. The afternoon was tricky, I also did Ranger Challenge, my second run of the day sometimes was a drag. I traveled twice, and on both occasions I missed Thursday Lab, but the other weeks where we were doing new or more important labs in Thursdays, traveling and missing was a no go. The simple reason was where was my scholarship coming from, the longer reason was balancing important meets that I wanted to compete in versus missing an important lab for a small meet.
To answer the question about dual scholarships, I don't really know. Although I am running, I walked onto the team. I would imagine it is dependent upon the program(s) (NROTC and swimming). A lot of aspects come into play with this, my issue personally was Title IV, where I was not on the roster during cross country season and made the track team. Logically IMO, taking the NROTC scholarship is both beneficial for you and your swimming coach, and here's why. By taking the scholarship for NROTC, this frees up money that the swimming program can use to recruit other top caliber swimmers. For this reason, my coach was more willing to work with me knowing that I was not financially a variable and I would be committed to running. The caveat to freeing up money and getting another top caliber athlete in the program that isn't you is again Title IV. This might be less of an issue for a Division III athlete, not because it's Division III, but rather less money in the program for a D3 school. Division I, coaches are trying to get bang for the buck when it comes to athletes and it is a lot more competitive, as you know. Again, all speculation on my part from my experience, take it with a grain of salt.
I feel like most of us can only speculate and give you a broad answer to the whole question you are asking. The best thing you can do is start emailing the cadre (who during the summer may not be that reachable) as well as the coach. They will have a definite answer to your situation. Also, I hate to say it, but if you had to choose one, do you see your self as a Commissioned Officer or swimming professionally after college. That is a question I am constantly asking myself when I have to decided between the two.