Allow me to possibly be the first, but definitely not the last in a long line of people who will recommend any other content creation software over SketchUp -preferably Maya or Blender- for what you are doing. The issue that, at least, I’ve dealt with dealing with SketchUp and exporting is that first, the chances are high that you got duplicate UV coordinates on your UV maps. For some reason, and this happened to me a lot too and a lot of others I’ve talked to, SketchUp really has a hard time parsing 3D shapes so it tends to assign the same coordinates to UVs on top of each other even when you take great care to unwrap your mesh delicately. Generally, SketchUp is great for concepting, but for modeling it’s Maya or the highway (at least for me) or Blender.
Likewise, the conversion process for Sketchup PRO is a little bit more graceful to FBX, I’m not sure if that is what you are using, but if you are going to get SketchUp Pro you might as well just get Maya and get yourself some pro tools. Just my opinion, again, nothing again SketchUp, this is all person choice. Unreal almost never chokes on meshes from Maya though so if you know you will do a lot of work between models and the engine, it may be worth investigating an alternative.
Also, this issue has come up about a million times and I’ve had to read through this same problem a lot for myself and others so I’ll just post the result of what others have gone through to solve their SketchUp issues and maybe that will help you out
Likewise, this video was super useful. This method only works for Pro, but I don’t know, maybe there is some basic tools use you are missing like cleaning up your mesh of tris or something that could be the difference between exploded vertices, missing pieces and wacky UVs. Good luck!