I feel your pain....from bitter experience..... but as has been suggested here, getting them involved in preparing the food with you can work. Aprons on, preparing vegetables for soup, stirring and cooking and blending worked for me with 2 very difficult 6 year olds.
Any kind of food preparation fires their imagination. Little savoury pancakes are usually irresistible. Food in very small portions, self-served onto small plates, and no pressure!
Eating at a table is a very good thing, and family meals together should be a pleasure and something that they look forward to. If there's a chance, eating with older children who love their food is a good encouragement to small 'picky' kids. Lots of chat, (not about the food) and they can end up just eating what the others are having because they want to fit in!
Picnic table in the garden, wraps, BBQ'd food on skewers they've done themselves, small items on sticks, cheeses, cold sausages, finger food, hard boiled eggs. Helping themselves. No desserts until some 'proper' food has been consumed and no eating between meals might sound tough but it's better that they're hungry at meal times and not in between if they're poor eaters.
Something they've made - and tried - to take home to Mummy : fishcakes, toad in the hole, savoury tarts where they've lined the little tins with ready rolled pastry shapes and chosen the fillings.
Doctors always say that no small child will deliberately starve himself, but, it's still very depressing to be around a child who doesn't enjoy your food and it certainly knocks our love of nurturing on the head! Persevere, they've possibly got stuck on the same old foods and they're just not interested in trying anything new. Food should be more than fuel and once you've got their attention, they'll probably be eating you out of house and home! ?
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