Just a little over a month since announcing their separation, Chad Kroeger and Avril Lavigne shared evidence of their relationship as it stands today. In two new pictures posted on Avril?s Instagram, the former couple is back in the studio working on new music together. In a new Instagram picture where she is seen wearing jeans and a t-shirt with her face hidden by a cowgirl hat, Lavigne writes, "YeeHaw! Writing with Chad today.