First of all, thank you so much for your interest in Cotton's TV commercials, specifically the spot you refer to below that features a remake of the Beach Boys "California Girls" with female vocals. This California Girls track was produced especially for Cotton's TV commercial with a music production company and is not a specific band. However, as someone else previously mentioned, an MP3 of the California Girls track can be found on Cotton's homepage (www.thefabricofourlives.com). Just click on "Download Our Music" link on the lower right hand part of the page.
I hope this has been helpful.