Why long letters usually fail
A four page letter asks the reader to spend an hour inside a version of the past written by the person they walked away from. Even when every line is sincere, the length itself is a demand on their time and their nervous system.
Short is not cold. Short is considerate.
Lead with the fact, not the feeling
If there is news, lead with the news. An illness, a birth, a death, a will, a diagnosis that is now hereditary information they are entitled to have. Facts are easier to accept from someone you are estranged from than feelings are.
If there is no fact, the message becomes an apology or a goodbye. Both are legitimate. Neither should carry a request attached.
The one promise that changes everything
Tell them this is the only message you will send. Then keep that promise. The single most common reason estranged relatives refuse to read anything is the reasonable fear that reading it starts a cycle they will have to end again.
Accept the likely outcome in advance
Most first contacts after long estrangement are not answered. Sending anyway can still be worth it, because the point is to remove your own uncertainty about whether you tried. Decide before you send that you can live with silence, and the silence hurts less.
When estrangement should stay
If the estrangement followed abuse, and you were the one who caused harm, contact can be a continuation of the harm regardless of your intentions. If you are unsure, that uncertainty is itself an answer worth respecting.