rich text editor behavior between browsers

We have a a lot of lists in our SharePoint Online environment which have multiple line of text columns that need to be set to either "rich text" or "enhanced rich text". Many of these lists are used to send data to public-facing websites (hosted in our web CMS [Sitecore]) using a "dataset connector" that our in-house developers created. This component reads the raw content of those fields, so however the text is formatted (using the controls in the editor toolbar) is how they'll be displayed on the website. The problem is that those controls/that editor seem to behave differently in different browsers.

For example, if you're using Google Chrome (which a LOT of our web editors use due to the wealth of debugging/troubleshooting tools available via extensions to Chrome) and you press the Enter key at the end of a line, it inserts a line break (<br/>) rather than starting a new paragraph (</p>[newline]<p>). At least, that's what it does most of the time. In about a hours worth of testing, several times, it created new paragraphs (which is the expected/desired behavior), but usually it just created line breaks. 

If you're using Firefox, it consistently creates new paragraphs. 

In Edge, the behavior is the same as Chrome, but the situation is a bit worse. In Chrome, you can use the 'Edit Source' button to get to the code view and manually make the necessary changes; this is not possible in Edge as there is no 'Edit Source' button.