OK, the instinct to reality-check what you're hearing from counselors is GOOD. Assume that none of your counselors have taken the DAT/MCAT or that they're qualified to counsel any premeds/predents except those that don't need counseling. What your counselors are likely trying to protect is your grades in the masters program, which could suffer if you divert your attention to the DAT.
Nothing's free, and the "free" anonymous advice you get on SDN is frequently laced with impatience and scorn. 99% of the people who post advice here only do so because we've invested a HUGE amount of time researching every last detail of the med school admissions process. So if you feel like we're throwing fish at you, you might choose to interpret this as an intention to get you to learn how to fish. IMHO.
I know nothing about the DAT, and there's no math section on the MCAT. That said, in my view, if your trouble on the DAT is math & gen chem, then unless you're taking math & gen chem in your masters program, no, your masters program won't help your math & gen chem scores.
Whatever your reason is for doing a masters program, whatever problem that's solving, it's not solving your DAT problem, imho. In your shoes I'd plan on finishing the program you started, with excellent grades. Then take another six months or so to prepare for a DAT retake. Ideally, take more math & genchem coursework and do it differently: get a tutor, go to a different school, do research on what teachers are the best. Also, pony up the cash to take a prep course.
Best of luck to you.