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I've done some dyadic (parent-child) analysis, and I must say they can be quite complicated. One of the most common challenges is in the sample size. In order to conduct analysis using SEM, you would need at least 200 or more. Imagine recruiting 200 dyads. For smaller sample size, you can manipulate your data and adapt liner mixed effect regression approach.

Grand-centering definitely helps your interpretation as it would standardize the unit of your scale and avoid implausible values. You may think it as adjusting for baseline covariate variables in longitudinal analysis. Everyone is starting at the same (statistically adjusted) baseline point (intercept), so the changes (slopes) would be more meaningful for dissemination. More traditional explanation would be centering dyadic age by subtracting the grand mean. Hence, the intercept represents the expected outcome for an individual in dyad whose age is equal to the grand mean. Without centering, the change (slope) would denote the outcome measure at age 0, an implausible value for interpretation, but plausible for statistical application. The same applies to anxiety.

My concern, however, is that your satisfaction variables are measured on a different scale. Some reviewers can raise issues as the scales are not directly comparable. You would have to justify the use of two different scales before thinking about any type of mean centering. There are several techniques you can use and provide empirical evidence of using two different scales. Item-level information and psychometric evidence extracted from IRT or Rasch model would suffice most of the reviewers. If IRT or Rasch model approach is not a feasible option, consider using variant of the latent change score model (requires large sample size).

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