かたわら

Indicates that someone pursues a secondary activity alongside their main occupation or long-term activity: "while (mainly) doing A, also doing B on the side."

Written, fairly formal style, common in biographies, profiles and news articles about someone's life or career. The clause before かたわら names a main, ongoing role such as a job or child-rearing, and the clause after it names a sustained side activity of the same person. ながら can also link concurrent long-term activities, but かたわら is more formal and explicitly marks one activity as primary.

• がてらN1「がてら」 means doing one thing on the occasion of a single action (often going out); both parts are one-time, concrete actions, the register is neutral, and it attaches directly to nouns without 「の」. It cannot be used for long-term side activities.
• かたがたN1「かたがた」 means achieving a second purpose along with some action; it attaches directly to nouns without 「の」 and carries a formal tone. 「かたわら」, by contrast, describes a long-term activity carried on alongside one's main occupation, so the two are not interchangeable.
• つつN2「つつ」 attaches to a verb's 連用形 and shows the same subject doing two things at once; it can also express the adversative meaning 'knowing full well... yet...'. 「かたわら」 refers to a long-term pursuit outside one's main work and does not describe momentary simultaneous actions, so the two generally cannot be swapped.
• ながら / いながら / ながらもN3「ながら」 is close to 「かたわら」 only in the sense of simultaneity: the same subject performing two actions at the same time; it attaches to ます形 with ます removed and is neutral in register. 「かたわら」 describes long-term side work in a more written style, so actions done simultaneously over a short period can only take 「ながら」.
• 一方でN3「一方で」 contrasts two sides or adds another aspect without ranking one above the other; its subjects may differ, it can attach to adjectives and 「名詞＋である」, and it also works as a sentence-initial conjunction. 「かたわら」 only describes one person's long-term side activity outside their main occupation and leans toward written style.

ながら and つつ can also describe activities pursued over the same extended period, but they simply link two concurrent actions, whereas かたわら specifically frames the first as a main occupation or role and the second as a side activity, in formal written style. がてら and かたがた attach a second purpose to a single outing or act, and 一方で juxtaposes or contrasts two aspects without a main-versus-side relationship.