Your first paragraph is fine and best. The rule is to start a new paragraph if a new person speaks.1 In your case, you are just relaying circumstances of Elisabeth's reactions in relation to William's verbalized statements, but she is not herself speaking. The final source I give below notes the big, basic rules of needing a new paragraph (I've added numbers here for reference, they are bullet points in the source):
- When you start in on a new topic
- When you skip to a new time
- When you skip to a new place
- When a new person begins to speak
- When you want to produce a dramatic effect
Going through that checklist in your example, you are still on the topic of the family business (#1), have not changed time (#2) or place (#3), do not change speakers (#4), and then #5 is really a stylistic determination. Do you want to emphasize the groan. If not, what you have as a single paragraph is fine. If so, then possibly making a new paragraph would matter. In such a case, you would perhaps say even less to make the effect more dramatic, so:
William said, “Sweetie, raising greyhounds is not easy. But it is the family business.”
Elisabeth groaned.
William continued, “Of course, you don’t need to take over the family business.”
However, a verbalized swear word technically does require the paragraph switch, as then you are changing speakers. So consider these two examples, depending on how you relay Elisabeth swearing:
William said, “Sweetie, raising greyhounds is not easy. But it is the family business.” Elisabeth swore under her breath at the turn in conversation. She rubbed the back of her neck. William said, “Of course, you don’t need to take over the family business.”
William said, “Sweetie, raising greyhounds is not easy. But it is the family business.”
Elisabeth muttered, "$*'+!".
William continued, “Of course, you don’t need to take over the family business.”
1 Some sources that note this:
