Is it considered unlawful to let the wife and children eat from the husband's lunch meal paid for by the company, or to let them eat with him at the restaurant in the evening while recording the cost as his missed lunch meals within the allocated amount (15 Euros), or for the husband to save money from the meal's value and record the full amount?

If the company's system does not provide your husband with lunch unless he is outside the home, then it is not permissible for him to take it while he is at home, because the conditions agreed upon in contracts are binding on both parties unless they deviate from the Sharia's scope. He must repent to Allah and return what was taken unlawfully to the company, or seek absolution from whoever has the authority to grant it.