Hello and welcome. My name is ***** ***** I'm a biologist with a special interest in trees. I'm sorry to hear of this accident.
If the trunk is splintered, I assume some bark has been torn off. Insects, bacteria, and fungi can enter such wounds. However, the old way of treating treat wounds with fillers and sealants have been found to do more harm than good. Within hours of being wounded, a healthy tree forms its own chemical barrier over a wound to deter these types of infection. Then it forms a barrier of scar tissue, sealing off the wound from the rest of the tree. Sealing or covering the wounds interferes with the tree's natural protective responses. You can read more about this process here:http://www.mortonarb.org/tree-plant-advice/article/705/trunk-wounds-and-decay-.html
For the wounds on the bark, you can use a sharp sterilized knife to remove any jagged edges on the injured bark. Just cut off enough bark to make the wounds smooth.
It would be best to cut off what is left of the branch. A two foot stub will be very prone to infection. Cut it off with no jagged edges. You can apply a fungicidal powder (not a liquid) to the wounds to decrease the chances of fungal infection.
Be sure the tree is well-watered during dry spells. You can also apply 2 pounds of 5-10-5 fertilizer per inch of trunk diameter measured at chest height. Mulching the tree may also help.
The steps above will be all you can do. If you have more questions, let me know in a REPLY. I hope your tree will be fine.
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