I can't have dinner outside literally means you are unable to eat your dinner outside (like, on the balcony, or in the garden). I can't eat out tonight - this is more typically said, if you mean you are unable to go out to eat (eg. at a restaurant)

No, "I can't eat dinner outside" sounds strange. "outside" means the outdoors...as in you can't eat in the woods or in the yard or at the beach or anything like that (maybe because of allergies or illness or sensitivity to the sun or something like that). I think more context could help (for example, are you trying to save money by not eating out?), but overall I would say "I can't eat out (right now)" or "I'm not going out to eat right now (where right now refers to a more general period of time instead of specific point in time = these days, at this time...but more colloquial) is a good option.

I think that is more correctly to say " Can't I have dinner outside ? " at least in your way of thinking.