We find it impossible to crack the almond shells on our almonds from two trees we have. What are we doing wrong?
I don't think you are doing anything wrong, some almond shells can be notoriously hard, depending on the species.
Maybe you are used to seeing/having soft shell almonds and your trees produce some hard shell variety.
Soft Shell Almonds
Hard Shell Almonds
Make sure they are ripe and dry enough (no fresh pulp around it), greener shells tend to be slightly sturdier and harder, and tend to get a bit more brittle/crumbly when they get older and less humid.
When I was a kid I used to eat fresh almonds straight from the tree during summer vacations at my grandmother's, and the only way we could crack the shell was literally hammering it with a small stone against the ground, and specifically on a hard surface, like a curb stone or something.
And even then it requires some skill, because hitting too softly won't crack the shell all the way through, hitting too hard will smash it completely crushing the edible part into a mush.
To do it at home a regular "pliers shaped" nut cracker should suffice, though it will require strength and more pressure then say a walnut for example. If you aren't afraid to break a door, put it near the hinges, between the jamb and the frame and slowly close the door, that should crack it open easily.
Be warned this can damage the door, break the hinges, and dent the wood, don't blame me!