JTS Geometry "Contains" not detecting point of an Inner polygon on edge of Outer Polygon

Touch is a bit odd when considered naively, but if you look at the JavaDocs you will see the problem with the way you are looking at it. (Emphasis added):

Tests whether this geometry touches the argument geometry. The touches predicate has the following equivalent definitions:

The geometries have at least one point in common, but their interiors do not intersect.

The DE-9IM Intersection Matrix for the two geometries matches at least one of the following patterns

[FT*******]
[F**T*****]
[F***T****]

If both geometries have dimension 0, the predicate returns false, since points have only interiors. This predicate is symmetric.

In your case the interiors of the two polygons do intersect so the polygons are said to not touch.

If you change polygon 2 to be "POLYGON ((1500 500, 1000 500, 1500 600, 1600 600, 1500 500))" then it does touch polygon 1.

Update

If you want to find polygons that are entirely within a polygon and not touching the boundary, I set up a quick test using the relate method and a 2nd polygon that doesn't touch polygon1.

WKTReader2 reader = new WKTReader2();
Polygon p1 = (Polygon) reader.read("POLYGON ((0 0, 1000 0, 1000 1000, 0 1000, 0 0))");
Polygon p2 = (Polygon) reader.read("POLYGON ((500 500, 1000 500, 600 600, 500 600, 500 500))");
Polygon p3 = (Polygon) reader.read("POLYGON ((500 500,  600 600, 500 600, 500 500))");

IntersectionMatrix relate1 = p1.relate(p2);
System.out.println("relate " + relate1);
IntersectionMatrix relate2 = p1.relate(p3);
System.out.println("relate " + relate2);

This gives:

relate 212F01FF2
relate 212FF1FF2

And there is a difference, so referring to the wikipedia page for DE-9IM, I can find out that this is saying that in one case the boundaries have a point (0 dimension) in common and do not interact in the other (F).

I don't think there is a named operation for this but you could use relate.get(1,1) >= 0 to check for interactions (False returns -1).