Hi,there are very many s'markets in & around Corralejo.Probably the easiest one for you would be the Eurospar on the lower level of the Las Palmeras shopping centre a mere 10 mins stroll away.Walk to the main street & head in the direction of the waterpark & it's on the right-easily seen. They have a varied selection of everything you will need & the prices are very good too. Ale/spirits are very cheap if buying local brands. Imported food/popular named brand items obviously cost more. No need for a taxi to the s'markets in resort but you would need one if going to the large Mercadona s'market outside of resort & that too is good value.
I'd have thought that carrying the shopping home would have been too much wherever you go if it's really to be a big shop. You'll be wanting soft drinks, alcoholic drinks, maybe water, potatoes, etc. will you? I'd personally advise you to walk to one of the bigger supermarkets and then get a taxi home. The Eurospar in the old town would be my choice as it has good areas for meat, fish, veg and bread/prepared foods, plus a café if you need a rest. The Hiperdino is also close by, for one of you to nip to if you're missing something. Taxis can stop briefly just outside or maybe they prefer to meet you in the underground car-park. Cashier/security staff will help with ordering one.
Leave the one year old at home with a parent and fill your boots at Mercadona, okay so you'll be gone a while and come back loaded but you'll benefit from the choice and savings. And a morning child free. Absence makes the heart grow fonder, you'll have a great time.
Eurospar at Las Palmeras is walkable, I believe they have a free delivery service if you don't fancy carrying stuff back.There are a couple of branches of HyperDino on the strip that should be reasonable convenient for day to day stuff.