Right-click source & source_copy and choose Model Parameter. This will enable other scripts/models to feed directly into this model.
The source will need to be a feature layer, not a feature class. You would need to run a feature class through the Make Feature Layer tool first.
I have just spoofed up this model to simulate what you are doing and it all works fine for me! I'm using ArcMap 10.6.1
The Merge takes 3 datasets, one with nothing in it and various M-aware levels, everything merges as expected.
This would indicate the source of the problem lies elsewhere. Modelbuilder often seems to hang on to old environment settings and ...