AVRs don't have VGA out so that would not help.
The simple solution is to let your TV do the video switching. Connect all you sources to the TV with HDMI. The TV should have an audio output. It would be a Toslink optical audio out or an RCA / 3.5mm line level or headphone audio out.
If the AVR has a digital input use that.
If not you may need a DAC to convert the digital optical to analog audio to make the connection.
If you need to get the set up display of the AVR on the TV you could use a video (composite or component) to HDMI adapter but for watching programming you would lose high definition if you used it all the time..