HAL really likes gentlemen to wear a jacket on the informal nights, but I doubt that they will turn you away from the dining room. My husband takes either his grey pants with a blazer or his tan dockers with a light summer weight navy jacket and a short sleeved shirt.
You don't' need 2 suits for formal nights - one is enough, but you may want to take 2 dress shirts and 2 ties, just to have a change. My husband takes a tux for fomal nights, so then he only has to take one other jacket for the informal night. A lot of men wear a golf shirt under their jacket - this is quite permissible.