Many of these looks are sarong style swimsuits, meant to fit and feel almost like a sun dress, and would have been made from woven cotton (without any stretch). Stretch cotton blends were in their infancy in the 1950s. Stretch cotton fabrics first showed up in sportswear, but not until later in the decade.
The easy-to-sew trend was a winner back in 1953, as evidenced by these adorable photos. Here's a one-piece halter suit with skirt style wrap made from four simple pattern pieces (shown above) that can be printed and enlarged to fit your dimensions, or your daughter's.
On this set, the one-piece design has been cutaway into a two-piece bikini style. These pattern pieces are almost modular in this sense... definitely inspired by tiki styles from Polynesia.
And here's another look borrowed from Claire McCardell, including a bandeau bra top and simplistic shorts, gathered and tied at the sides. Both the design and the chartreuse color of this bikini is classic to 1953.
And oh-my-goodness, cuteness galore in these wee swimsuits for the little ones. The bandana print is actually made of two Western style scarves, seamed once and tied halter-style at the neck. Ready for some sun & fun!