Act egoism and dispositions

In class when we were attempting to make act egoism out to hold the same ideals of common sense morality, we discussed the important of certain dispositions in close relationships. The idea that was put forth was that in order to have good close relationships with people that give us the best mental states and wellbeing we must put ourselves out there to the point that we'd be willing to sacrifice our lives for it. Further, since there is a relatively low chance of us ever having to actually do that, it is a good chance to take. That is to say that it is worth the risk of having to sacrifice one's life for a friend in order to have that friendship. One thing I was wondering in class and never got to discuss was whether that ended up being a form of rule egoism after all. In this case, the rules that one would be following would be the dispositions themselves. Act egoism in the way I interpreted it involves following the action that is best for someone. In contrast, rule egoism is following the action that adheres to the rules that tend to result in what's best for someone. In following the disposition one has towards his or her close relatives to the point of self-sacrifice, aren't they simply following rule egoism, in which their act follows the rules of the disposition. I started to hit this point when I questioned the ability to change ones feelings on a dime. If one truly follows act egoism to the fullest, I still have a hard time believing that they wouldn't be able to change their dispositions on a dime. Act egoists are supposed to act in their best interest, not based on the rules of what would normally work out best. I feel that the dispositions one has to be willing to sacrifice their life for someone close to them is simply a rule that the rule egoist must follow, but not one that a true act egoist would. Maybe I'm misinterpreting the distinction between act and rule egoism, but that's how I tend to look at the two.