We had a similar experience when our daughter and her two toddlers moved in while her husband was overseas. It was beyond price to have that much grand kid time.
Your response and the couple right before gave me some hope for Freepers. The others were really shocking. Family pulls together and in doing so reveals the meaning and joy in life.
Instead of letting your children know you expect that they will be deadweights and leeches unless you demand they pay rent why not be genuinely interested in them, and the way you can help them on their path. Why not have faith that they will grow toward the light and be a witness to your belief in them and their abilities. If you can afford to help them get a proper start through extra education and a savings in rent/expenses why wouldn’t you be glad to do so?
Will that dishonor you or them if given gladly, or will it enable them to have a better start so they can accomplish more of their dreams and ambitions. If they are not working towards something I would not help them avoid responsibility for their destiny but to help through a legitimate rough patch or to let them save for a few years while starting out I would certainly help if I could do so, without a second thought.