It is highly unusual for a web site, even a web mail site, to require a double click to do something. That makes me think your husband is using some unusual method to get mail. The only thing that occurs to me is OWA (Outlook Web Access), which doesn't work well with iOS devices unless it's set up just right.
The other possibility is that the site is using Flash or Java for it's online mail client. In that case you might be able to use one of the Flash enabled browsers. Puffin has a trial version he can try his site with. It includes a trackpad simulator, so double clicking is possible.
That said, sometimes tap and hold will get results on items that usually work by hovering or double clicking.
Without more details (and probably even with) all I can suggest is for your husband to talk to the universities IT staff and see how they recommend connecting with iOS or other mobile devices.
If they don't have an approved method, then someone should be suggesting they take a closer look at what's happening in the world and get themselves a plan to deal with it.