Can one use both parametric and nonparametric tests?

I think this is where I should post this question. Sorry i am new.
I was wondering if someone could tell me if i am on the right track.
In my doctoral thesis I have an experimental group of 15 children with learning difficulties and a control group of another 15 children, matched at random. I am going to administer a programme to the experimental group.
Before the programme I administered 3 tasks to the experimental group and control group and I repeated the tasks after the programme.
I am using two way ANOVA to see if there were main effects of group, main effects of time and interaction effect. If i find an interaction effect I would administer a t-test.

Since I am not convinced that I should use parametric tests I also decided to further data analysis by using nonparametric tests (Wilcoxen and Mann-Whitney) to compare these results with those of the parametric tests. These would confirm and support my parametric results.

Is this acceptable? would it look stupid in a thesis if I do something like that? cause actually I would like to include the ANOVA but I want to play safe cause I do not want examiners to note that the assumptions for using parametric tests have been violated. So I tried to be safe and cautious.
THanks for any advice and help.
I think normally one way to go should be enough. But the non-parametric tests have not so much power, perhaps you find no significance. Did you check on normal distribution and variance homogeneity? And what what data type you have: Count data or measurements? Here data transformation may help and you can use the more powerful ANOVA.
Hope this helps
yes hobglobin - that helped a lot. I will be using only parametric tests now cause using the Kolmogorov-Smirnov test all data was consistent with normal distribution. Thanks again.