In your 3-way ANOVA with one between-subjects factor (group) and two within-subject factors (condition and time), you have already shown that the interaction of group x condition is statistically significant. I don't understand why you would want to run a separate two-way ANOVA again because such an analysis would essentially give you exactly the same result.
To confirm such an equivalence yourself, you may try the following two approaches:
1) Obtain for each subject the average value between the two time points for each condition, and then run 2 x 2 mixed ANOVA (one between- and one within-subject factor).
2) With a 2 x 2 mixed ANOVA, the group x condition interaction is basically a Student t-test. You can get the difference between the two average values above in 1) (one for each condition) for each subject, and then run a two-sample t-test on the condition difference. In other words, the group x condition interaction shows the group difference of the condition difference.
Furthermore, to tease apart the specifics of the interaction, you can do the following:
(a) Run 2 two-sample t-tests, one on the average value for each condition; Or perform 2 paired t-tests for each group on the average values for the two conditions.
(b) Run 4 one-sample t-tests, one on the average value for each condition within each group.
With these tests you can use plots as shown on this page to understand the interaction.