Nat,
I believe the older man in your dream is your father, not the father you know consciously but the unconscious father you wish you could have known. The young boy would be your undeveloped masculine due to a lack of a good relationship with your father {bad fathering}. In real life your father gave you little emotional support {how does the summer season fit in with your relationship with him?}, he was an outsider, perhaps always promising something only to apologize for not giving it later {or this may be how your unconscious looks at him}.
Something is locked inside you {car}. something to do with the father and your inner masculine. It probably is the relationship or lack of with your father. It could be something else. Look back at your 20s when you had the dream and see what was going on at that time. It may have been an actual experience or it may have been a realization of something from your past {locked away} that you began to remember.
There does seem to an element of 'promises' to the dream. That may involve the hopes you had for a good relationship with your father, the secret, mysterious island {the island is a part of you}. The sick mother probably points to actual physical conditions on her part or/an he inability to help you in the relationship with your father. Was she passive when it came to that relationship? What was the relationship with your mother. Was she 'needy' in her personality {'she needed me'}?
Was there a time in your 20s when you and your father had an 'enjoyable' experience? That may be why you are now remember this dream. Such an experience would be a small part {island} of the whole relationship with your father, a promising one {promises}. The attention would have given you made you happy and brought about promises of restoring your whole self.
The last part also seems to be about a father you wish you had and an experience where he at one time fulfilled that wish {in your 20s?}. But you are married to reality and whatever comfort he gave {ice cream} soon melted away. As for your mother he sickness may have been an inability to help with your relationship and/or contribute in a way to fill the void. She may have needed you as much as you needed her. But she was 'sick' and unable to help.
One last thought. Other than a lack of good fathering was there anything about the relationship that was abusive {other than psychological?}. The locked car could be pointing to that but in the dream it does not specifically do so {which would suggest there wasn't}. But to cover all the possibilities it is something to look at.