It's an interesting question. In terms of where the real power (economic, social and political) lies, the DR is not really a matriarchy, but there are some interesting exceptions to the rule.
One is the fact raised by Dolores that many families here are headed by women. I believe the statistic is about 48% across the Caribbean. This happens as a result of desertion, not just divorce or family break-up but because of the migration from rural to urban areas and overseas. Most of these women-headed families are concentrated in the lower end of the socio-economic scale, and have limited economic power or political and social influence.
OTOH, economically and politically there are some remarkably strong women in this country. There are caudillo-type politicians like Lila Alburquerque and Milagros Ort?z Bosch. There are high-profile and influential business leaders like Elena Viyella de Paliza - and she is not a one-off case. Many top judges, journalists, doctors and lawyers are female. These are good role models for strong, qualified and high-achieving women in DR society, and national heroine Minerva Mirabal who was an intellectual as well as a revolutionary is also worth a mention.
Another encouraging trend is in education - most university students are female, so unlike certain other developing countries where girls are largely denied an education, the DR performs well in this sense.
The mother does have a special place in the Dominican family - she is placed on a pedestal and accorded a great deal of respect. Or is she? My impression is that especially with regard to the older generation, much of this respect is superficial, and that no one really listens to much of what she has to say. She is adored and feted, but ultimately her role is to care for her brood and not much else. In women-headed households the son or another male relative like a son-in-law will often assume the real position of authority in the family anyway.
It is likely that this will change as educational levels improve. The signs are there.