I love kidney beans - like little fluffy clouds of potato, wrapped in a purple prose... Sorry skin.
OP, I was veggie for 20 years, half of it before Quorn came out - which is probably their best bet with regards to mince.
However, my daughter and I love a vegan bean chilli...
Kidney beans, butter beans, chick peas, black eyed beans... In with the tomato based chilli sauce (tomatoes, garlic, onion, chilli powder), whilst it's cooking, mash them down so sauce becomes thicker and the beans become less recognisable.
Add red lentils by all means - work as a thickener and more protein. Just lob a handful in because they bulk out a lot.
Season to taste, and mash to texture - voila vegan chilli.
But if your kids don't like beans I'd just use Quorn... Or point out that vegetarians eat lentils, pulses and vegetables lol.