Have you pruned them at all since you got them? How old were they when you got them?
With formative pruning, you establish the shape/form of the tree and that's crucial to its future. It might have helped with the snapping because you do remove quite a bit of the new growth each year to take it back to a bud, which ensures it branches and doesn't just go upwards. For the shape I prune to, you take out the central leader and ensure a nice wheel of branches going outwards. This should mean you have shorter, thicker branches in the centre rather than long, skinny ones. You don't need to be brutal - the only time when that's appropriate is when you've got a very old or weak tree than needs regenerating - but you do need to prune it properly. Without knowing how you've pruned it so far, it's hard to give specific advice but for a three year old tree you'll be looking to take one third to two thirds off new growth, cutting back to an outward facing bud - as well as removing some of the growth that is going vertically upwards, anything that is crossing or pointing in to the middle and any dead or damaged branches. Your aim is to get air and sun to all parts of the tree, whilst leaving some fruit buds on too. Bramleys can tend to be tip bearers which means cutting back all new growth might limit fruit for next year but I think that generally applies to older Bramleys (and I've got some which are probably a hundred years old or near enough and they're not exclusively tip bearers).
You can also remove some fruit if you think there's a danger of the branches breaking. If it has set a lot of fruit, it can be sensible to remove some fruit from each group because that allows the remainder to ripen properly.
I'd be surprised if baby trees have lichen on although it's not a concern & is generally a sign of pure air. You've more likely got moss which may be another sign it's not well pruned. You need to keep the centre of your tree open to allow the air to circulate (another reason to remove the central leader and any branches that grow in towards the middle). This in turn means moss won't be as happy there because it likes a damp environment.
Finally, if you haven't got what you expected, can you go back to whoever sold you the trees? Certainly if it's a decent nursery, you should get some compensation if you've ended up with a completely different variety to the one you were intending to plant.
H