Bayahibe fits your criteria.
1. relatively safe Yes
2. close to excellent scuba and snorkel spots - yes. do a google image search for "bayahibe dive map". good snorkeling off the beach. 3 or 4 good dive outfits in town.
3. can live walking distance to beautiful beaches for under $1000 a month all accommodation in Bayahibe and Dominicus is within walking distance of the beach. yes under $1000 pm, average 600 for 2bd apt. There are also apart-hotels that have apartments for rent long or short term.
4. able to do our shopping in town Yes local supermarket is pretty well stocked. easy to find fresh fruit, veggies and fish. Decent bakery (Trigo de Oro) in Dominicus 5 minute guagua ride away. 25 minutes drive away is La Romana with pharmacies and large well stocked supermarkets - Jumbo, Iberia, PlazaLama etc. Several inexpensive restaurants around the 2 bays.
5. good internet connection (husband works online) yes