I see two problems in the current situation, and one common solution. If two dojos have merged, then that implies a mixing of the two beliefs and goals, and even names (or a new name selected entirely). It sounds like the 'home' dojo rather wants to assimilate the 'visitor', and the 'visitor' is resisting. Merging only works if both sides are willing to compromise and perhaps change, like a marriage. Demanding one subject itself to the other rarely is successful. While the visitors may be taking advantage of a roof over their head, I assume they are paying for it as well, and the home dojo probably didn't mind the bolus of new students.
Students who do not attend classes where self defense is stressed, when that is not their goal, are not disrespectful. They are voting with their feet. If the visitor dojo leaves and a lot of the home students leave with it, that is also voting with their feet. Enough voting might prompt a reevaluation of the goals of the home dojo. The two problems: not a clear understanding of whether this is a merger or a (somewhat hostile) takeover, and values that sound rather divergent. If the two groups are not interested in compromise, then the visitors should find a new place, and the home dojo should wish any that leave, including home students who are voting with their feet, good luck.
Oh, and I was in a club that belonged to one organization, but one of the instructors belonged to another---and it was the best experience I have had. Every one (including instructors) was respectful of the others' teaching and values, students were exposed to a variety of methods and beliefs, and there was a lot less politics than in my current, only one organization, dojo. So two different teaching styles can easily exist under one roof, as long as egos make room for it.