We have visited the Dom Rep four times. Two trips have been to a lovely little island, Cayo Levantado, with only one hotel, magical; excellent food etc, but no use to you as it is adults only. The other two trips have been to the Bahia Principe el Portillo, (part of the same chain who run Cayo Lev), once with just DH, and last August with the full tribe of DSs and DGcs. It is on its own, not in a complex, with the most stunning beach, huge rooms, excellent food, fabulous for kids. We would happily have taken them there this sumner, but First Choice, the only UK operator who offers it, have changed airports and the transfer is now four hours not one. If you can cope with this, and we did it on our first visit, I am sure you would love the hotel, check out reviews and photos on Trip Advisor. We have booked to take the kids to Mexico instead this August, but with the Grand Bahia Principe chain again, as we have found them to be absolutely excellent and reliable. It is in a big complex though so hoping for the best. If you don't fancy the transfer to El Portillo, have a look at the Punta Cana area, but I think most hotels there are in a complex or form a continuous line along the, reputedly wonderful, beach. I'd tend to avoid the Puerto Plata end of the island. We really loved the Dom Rep, plenty to do and see, very good value but be wary of suspiciously cheap hotels, or take industrial quantities of Immodium. We had no problems in this area.
The other Riu hotel is the Mambo - have been there twice and 7 times in total to the DR.
My favourite hotels are from the Iberostar chain - the best being in Punta Cana (the Dominicana, the Bavaro or the Punta Cana). All 3 share a fabulous white sand beach. If you want to head for the North Coast, the berostar Costs Dorada is also very good.
It was more of a progression to match our income. We started with a few years in Turkey, then lots of trips to the DR, then other caribbean Islands, then finally the Maldives. Now we have two kids we tend to go a little closer to home, although we did take dd to the Maldives when she was 3.9 yrs.
Sounds quite like us, though there was plenty of camping to start with. Getting into the habit of taking grown up DSs and the DGCs away in the summer made the Maldives very pricey, though we had three family trips there. I think it is a perfect environment for small kids, regardless of the disapproval of honeymooners. It is so safe and peaceful and the beaches are simply paradise for children. DH and I Are going to Jamaica in March, first time so hoping it will be OK, then Mauritius in May. Significant birthday year for me. As good an excuse as any.