Being in a long-distance relationship is very hard. I'm not saying it can't work, I'm just saying it takes a lot of work. It sounds like part of the reason you guys might be having troubles is because you two are feeling a bit insecure?? You feel insecure that he won't just call and check-in and then he's feeling insecure b/c when he does finally call, you might not be able to answer (like when you were eating with your grandparents).
A relationship is absolutely nothing without trust, and also you both have to accept each other the way you are. If there are things about him that annoy you to no end, you have to decide whether or not you can live with that for the rest of your life. And vice versa. Now, I will tell you this...when two people love each other and they know that a certain thing or another annoys the other person, they try to improve that about themselves to make the other person happy
So, my point is that you can't change someone, but if they love you, they will try to do what it takes to make you happy. Every relationship has rocky times...
It's not the arguments, it's how you come out of them...You should come out of them stronger than ever.