So basically you are performing a MANOVA to examine mean differences in two types of attention latency across two stress and two resilience conditions, as well as their interactions.
To answer your question, is this allowed? Yes, it's allowed. Is it the best possible way to address your problem? Probably not!
There is a certain reason why you run a MANOVA and not two between-subjects 2-way-ANOVAs. It's the same reason why you shouldn't brake down your sample in four subsets according to the interaction level your subjects belong to. This is reason is minimizing Type I error. For every additional test you run, you introduce a new source of Type I error.
Instead, run a MANOVA as you suggest and interpret the main effects of stress, resilience and their interaction. SHould you get a significant p value for the interaction term run post-hoc tests to identify which combination of conditions differ significantly from each other with respect to your dependent variables. Keep in mind that even if the p value of the main effect of the interaction term is significant (p<.05) there is a chance your post-hoc test might not identify any of the conditions as differing significantly from each other with respect to the mean latency values. Should this be the case, it will coincide with your observation of no significant findings after splitting your sample in 4 sub-sets.