I've seen two different stroke orders for this character:
Which one is more "correct" or widely used?
It seems to me that the fourth stroke in the latter picture is incorrect, and that it should be part of the second one. Is this right?
I believe for 印 the 1st one is correct. 氏 is written in this order: . The first 3 strokes are exactly same as those first 3 stroks in 印.
Consider the following characters: 卯, 留，齊(齐). We finish this part first, , then add the next strokes, which are 丿, 丶, and ㇏ respectively.
But if you make the font of 印 like this, the 2nd order in your question is correct.
The discussion above is for 楷书. But the stroke orders are sometimes different for 行书 or 草书, in order to write faster. See the following examples:
Take as an example, the stroke order is:
The first one is right. Our primary teacher had taught us with punishment. Believe me