Yes, the White House communications director must have had a fallout with Trump in order to resign that quickly. The person wouldn't have agreed to take the job at first if they hadn't thought through all that the job entailed. The person was probably thrilled to be offered the job. They wouldn't have given it up voluntarily.
Instead of jumping to conclusions about why Mr. Trump's communications director resigned, we should accept his explanation. His wife is pregnant and due in January. It is probably more likely that upon further review of the actual requirements of the job he decided that it was more important to be with his family.
Whether or not you believe in Trump or voted for him, one has got to rationalize the different sources of information. That, along with the sources' motives and whether society ever gets the truth when discussing matters of a government department of this level.
I prefer to just think about it as something that has happened, probably will stay that way, is a reason for gossip and the how in the heck this position matters to the American public.
Jason Miller's excuse that he wanted to spend more time with his young family and pregnant wife did not sound particularly credible. Yet, it seems unlikely that his reason to decline the role were to do with a personal falling out with Donald Trump. It is more likely that he feared his professional career would be damaged by an association with Trump's presidency.