There are WAY too many variables to say if they are going to hurt your chances. It really depends on your history in college, as well as your DAT scores.
I mean no harm, and I think it is honorable to try and help family(I come from a financially broken home, so I understanding making sacrifices to help stay afloat), but dental schools won't care how good of a person you are if you made absolutley awful scores and have a bad GPA from college. While I am sure the admissions board will admire your actions, they look at applicants to see how prepared they are and if they show signs of doing well in their school, eventually becoming a dentist in 4 years.
If you have great scores and a great GPA, and your DAT scores are still relevant to the school, you shouldn't be turned away from taking 3 years off from school.
Its far more important to be personable and kind as a dentist, rather than a whiz who can make a 25AA but is introverted and antisocial. You get the picture.
You have an outstanding DAT score, but a mediocre GPA. Some people would be discouraged if they had your GPA, and would consider going into a Master's program, but I think if you have shadowing experience and if you know you want to be a dentist, and for the right reasons, you very well could shine in interviews and definitely get into a school. Probably not the top tier schools, but then again, this is dental school we are talking about. Doesn't matter if you went to Harvard or Meharry in my book, you're still a DDS/DMD(mostly). The same is not true for medical schools, however.