Implications of descriptive statistics on parameter estimates I am working on my dissertation and a question dawned on me after I ran my analyses. 
I studied whether the interaction between marital conflict and gratitude on mental health differed between first-married couples and remarried couples. 
Descriptive analyses revealed significant group differences between all the variables means of each group (remarriage couples reported more conflict, lower gratitude, and lower mental health). 
I then conducted separate path models for each couple type (first married couples & remarried couples), and when a significant interaction was observed for one group, I constrained the interaction term estimates to be equal across groups (a form of a 3-way interaction).
Now to my question. Would the mean group differences observed among the study variables affect my ability to make between group comparisons in the path models, specifically the interaction term estimates?
Thank you for your time.  
 A: First, in your 4th ¶, you indicate that you observed the interaction ($p<\alpha$) for one group, and then "contained the interaction...to be equal across groups" which suggests not a 3-way interaction, but the exact reverse...you've constrained the 2-way interaction term to be equivalent for both groups.  A 3-way interaction would allow this value to be estimated freely for each group.
Second, to address your main question, it is not the mean group differences that are the issue, but whether there is a moderation effect due to marriage status (first-married or remarried).
What you want to do is run the model
$$MH \sim C + G + C\times G + S\times C + S\times G + S\times C\times G $$
With this, if $S \times C$ is significant, this says the path from $C$ to $MH$ is different for the two groups; if not significant, then the path is the same (and the term can be dropped from the model).  The same logic applies to $G$ and the interaction.
Alternatively, you can run a multi group SEM to see if the paths can be set equal.  (Happy to provide details on that if needed.)
