Every serious livestreamer needs to invest in a decent video mixer. The Roland V-02HD MK II is worth a look. It supports 2 x HDMI inputs up to 1080p60. It comes with a T-bar, push buttons, and an optional foot-pedal switch for easy control.
The V-02HD MK II can be controlled with an iPad app. It comes with PiP and various transitions and visual effects. It plays well with Roland’s AeroCaster Switcher for iPad. You can find out more about it here.