Mrs Katz, the only way to encourage children is … to encourage. Compliment them when they keep their shoes on, and avoid crititiscm. My suggestion to you is that five mminutes after they come home thank them for keeping their shoes on, and you might find them still on their feet much later.
Regarding you mother inlaw, the only way to win a machloikes is … to give in.
Just by the way, i don’t mean anything personal, but she probably tells your children that shabbos shoes are a waste of money because she realises that a polite suggestion to you will be ignored.