Your first paragraph is fine and best. The rule is to start a new paragraph *if a new person speaks*.<sup>`1`</sup> 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):

 >1. When you start in on a new topic 
 >2. When you skip to a new time 
 >3. When you skip to a new place 
 >4. When a new person begins to speak 
 >5. 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.”

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<sup>`1`</sup> Some sources that note this:

 - http://www.writersdigest.com/tip-of-the-day/write-like-a-pro-master-the-rules-of-dialogue-in-writing
 - https://www.dailywritingtips.com/dialogue-dos-and-donts/
 - http://www.saidsimple.com/content/100835/