So a while back I was traveling on shadowmere and I saw some bandits! So I get off Kill them, go inside and raid their belongings. When I come out shadowmere is dead

Now It's been long enough where he would respawn alive in that spot but I can't find the spot!

It was towards the south west corner on a high up but pretty flat hill. The bandit camp was a trapdoor in the ground with not even trees around it.. It may have been quest related. I can't remember. If anyone remembers this spot or comes across it please let me know!

Doesn't the horse respawn back where you first got him?

Happens to me regularly: from the uesp wiki:
Note use the duplication only in last resort. Prefer moveto.
There are mods that make him essential.

No, it respawns where it died or disappeared.

I think he respawns where he was killed. I haven't used him in a long time, but I do remember (right after mounted combat became available) that he was killed outside of the fort across the lake from Riften. I had completely given up on him until I ran by that spot some time later and there he was.

Hmm, I have gotten Shadowmere and I have not used him. He just follows along as i fast travel. At least the other horse the game stuck me with had the good sense to go run up to a giant and get killed so I did not have to deal with it.