Julie
there are a few separate issues here. FIrst, I agree with Gordon. Incorrect Z values in drone GPS data is a well known problem - I've documented altitude errors up to 100 m for some very common drones. If you do not use 3D control points, your output Z values will never be accurate. (Having said that, the DSM and DTM from the same project should be self-consistent, so even if not absolutely accurate, the relative accuracy should be good, with a critical dependence on content).
I think the more important issue is that what you're seeking to do is really not possible with optical imagery. Images cannot penetrate through canopy the way lidar can, so you're not going to get valid ground samples under the vegetation to create a DTM. In addition, the DTM created in this manner is an *estimate* of the bare ground, and created in a fully automatic manner. Without editing, it's not going to successfully eliminate thick vegetation canopy. This DTM is really intended to be an elevation base for orthorectification of imagery, but not of the quality needed for hydrographic analysis or detailed canopy height measurements you're seeking to make.
If you want to proceed with using drone imagery to do this work, it will be more complicated but you can get a good estimate of the vegetation height (presuming this is your full study site. If this is just a small sample and the full project is 100x or 1000x this area, this will not be feasible).
I wouldn't use the auto generated DTM at all since it won't adequately remove the low, dense vegetation. You'll have to manually create a DTM. If you can make a copy of the DSM, and draw polygons around the open 'pits' to mark areas to *retain*, then zero out the rest of the DSM and then interpolate to fill the erased areas, you'll get a pretty good estimate of the DTM (although this would not reveal any hidden stream/drainage channels that may well be there). Also note I'm assuming those 'pits' are the true ground and the vegetation between them that's ~1-2 meters tall should be included in your vegetation height output...?
If you have ArcGIS Pro and the Image Analyst extension, this DEM editing can be done with the pixel editor. If you don't have Image Analyst but you do have Pro, you could do this editing with the point cloud.
Let us know if that manual editing is feasible and we can advise further.
Cody B