Awesome- thanks, I'd missed that there was the option of different CSS for desktop & mobile. That's all working a treat now.
In case it should help someone else in the future, I did have to make a small change to the mobile CSS to get the icon positioned correctly:
.instaicon a { background-image: url(/wp-content/themes/lay-child/images/Instagram-16x16-1.svg); background-repeat: no-repeat; background-position: 23px; background-size: 20px; }Really appreciate your help :)