Not counting mobile apps, I haven't used a non-browser based email client for about two decades, so I can't help you there.
But another possible solution, which I admit may not be a good fit for her, is to consolidate her accounts either by setting up a rule to automatically forward all emails from one account to the other, or by getting a third email account which both of her current accounts automatically forward to. Maybe one that has a "desktop" client* and iOS app. Then she will only need to use the one account that is receiving all the emails.
* Many websites will let you "install" the website as a "desktop app" which is basically just a simplified browser window that only loads that one website. Any external links open in the full browser. Perhaps you could "install" the browser-based email client as a "desktop app" for her to use, and of course use the email service's app on iOS.
