I need to know if this is possible.

Harry's invisibility cloak can't be summoned by the Death eaters in DH (when they land in Hogsmead it stays still) but does this mean that Harry can't summon it?

I'd rather like James to be able to summon the cloak and was hoping that as the true owner then only he could do so but if there's canon evidence to the contrary then I'll forget that idea.

Also thinking ahead:- Do you think Harry's children would all receive the same protection from the cloak (as heirs of Ignotius) or only the one Harry bequeaths it to?