A short list, and worth knowing precisely rather than approximately.
Haleʻiwa Aliʻi Beach Park, in town. The most protected swimming close to Haleʻiwa, with a lifeguard tower, restrooms and a proper lot, and calm enough on most summer days for young children. It is also the Triple Crown's opening contest venue in November, which tells you it is not always like that.
Three Tables, at the southern end of the Pūpūkea reef. In summer the flat rock slabs create shallow pools and gentle water between them, and it is the easiest reef snorkelling on the coast for a first-timer of any age. Water shoes, an adult in the water, and check the tide.
The tide pools at Shark's Cove, on the Pūpūkea side. In summer these are genuinely excellent for small children: ankle to knee deep, full of small fish, and separate from the open cove where competent snorkellers go. In winter they are not a place to be at all.
Waimea Bay, in summer only. Wide, sandy, lifeguarded, with the rock at the north end that older children queue to jump from. In winter it is the most dangerous beach on this list.
Mālaekahana, near Lāʻie. Sheltered by the reef and by Goat Island offshore, with a long sandy shallow, restrooms and a campground. The calmest family water on the coast, and it works more often in winter than anywhere on the Seven Mile Miracle.
The coves beside Turtle Bay. Protected by their orientation and a reef lip, these are the realistic winter swimming option here. The beach is public, like every beach in Hawaiʻi, and the resort marks access stalls, which are limited and go early.
Not on the list, deliberately: Ehukai, Sunset, Laniākea, Mokulēʻia. All are fine to visit and none of them are children's swimming beaches.