You said that you can't clear down if it calls a landline, I would be starting to diagnose from there to make sure that is correct.
I have known some devices not to sent DTMF while in a call, you have to go to another menu or need some third party app to enable this.
If it requires an app this may have it's own controls in settings or require your volume to be higher, will difffer from device to device.
Making sure landline to landline (or even the old Iphone) works first would rule out a fault elsewhere.