In the Marbella, San Pedro and Estepona area you have plenty to chose from - but you have in Estepona a Carrefour and in Marbella, San Pedro and Estepona no end of Mercadona supermarkets. Plus, of course, there are Lidl supermarkets in these areas.
Oh dont forget Al Campo at the Cañadas shoping centre at Marbella although I have never been a fan!
All have good quality 'own brand' lines
Sunday Opening - can vary from place to place but generally supermarkets are permitted about 13 sundays a year to open on.
This year most are staying open till about 12th September and then will open again for a couple of weeks over Christmas.
Most will have a sign up telling you the opening days and times. Certainly Lidl and Carrefour will be open but Marcadona is a more old fashioned 'very spanish' type of business and not all shops open on Sundays.
Hope this helps