/u/pixelphantom is correct. How the different timeframes gets interpreted is up to the viewer. To me, the get shot in the stomach is present, and the one where she rides away is the past.

I have to watch it again, but I am not sure, that there is two timelimes overlayed and two gun shots.

How I watched it was like this:

Dolores is in the present as she arrives at home, after talking to the sheriff in town (the one getting backup for Teddy). So watch the scene as all in the present, except for a series of 3 flashbacks ending with the narrative cutting to the past in the 3rd flashback and never returning to the present.

Flashback, for Dolores, means she is accessing a part of her memory bank and playing the data there in her head.

So Dolores is in the present as she comes up to her dying father, she sees a flashback of her original father (could be any part of her memory bank up to 10 years prior, the time the original father was playing the role)... following on back in the present, she is dragged into the barn by Rebus, she then sees a flashback of MIB (could be part of any day up to 30 years prior, but most probably recently because MIB has aged)... following on back in the present, she is able to kill Rebus and runs out of the barn and then gets shot, as she is dying she sees the 3rd and final flashback of being able to avoid it an get away by horse (this was more than 30 years ago, at the time of William) [Narrative stays in the past and DOES NOT RETURN to the present, and final scene she meets William]. The next time she wakes up can either be a past loop (getting killed after meeting William) or present loop (having been shot in the stomach and died).

Dolores can pull the gun trigger before Teddy try to teach her because in the past she gained the ability before.

Dolores looks surprised that she is not shot in the stomach because, even though she ran away 30 years ago, prior to that point she was shot dead many times on previous loops.

Is there any holes in this line of thought?