The new Skype is a mixed bag in terms of whether it's better or worse. Accessibility wise, I miss the rotor actions, but other than that the interface feels much faster especially if scrolling through large, busy chats.
Visually, the new Skype is trying to kind of be like SnapChat, there 's a lot of emphasis on sending pictures, making public highlights of your day, and of course huge emojis. Because everyone's doing that now. A lot of things were thrown out as a result, IE the concept of various statuses like On-line or away, but because of a rather large backlash they r slowly making a comeback as part of the new design.
All that aside, using it for calls isn't very hard at all. When you open the app, you land on a screen showing your most recent chats (which also includes outgoing or missed calls). On pretty much every screen you always have a "people" button at the top that opens your contact list. So you just double-tap that, then you can just flick through all your contacts to find the one you want, and double-tap on him/her which will open the chat with that person. And one of the first things on the chat screen is the button to make a call.
Also, Skype has full support for CallKit and Siri integration. So, if your Wife's phone runs iOS 10, if you go into the phone app you will be able to see any missed and outgoing Skype calls on the recents tab, just as if it was a regular phonecall, and you can return them from here as well. You can also make calls just by finding a contact in the phone app, and if they set up their phone number with Skype you'll see an option to make a Skype call next to regular phone and FaceTime options. And finally, you can use Siri voice commands to make Skype calls or send chats. The commands for it are pretty much what you'd expect, Call "Dark" on Skype, or, Skype "dark" should all work and just make the call.