尿 works as both noun (urine) and verb (to urinate). The reduplicated 尿尿 is the casual childish form used with toddlers.
register
Standard Mandarin reads 尿 in all modern compounds. A second reading 尿 survives only in dialect words like 尿泡 and 尿脬 (bladder); don't use suī with general compounds.
Inner 水 — pictograph of flowing water. With the body radical above, this is one of the most starkly literal compound ideographs in the script: a body releasing water = urine. No phonetic component; both pieces are pure meaning.