Grammar for $L=\{a^{i+1}b^{i}c^{2j}d^je^{2j}|i,j>0\}$
Your answer is correct.
The alternative with $E\to ee$ is incorrect, as it might generate 'ee' in between 'd's. You must first shift all the E's to the end and only then make them into $ee$.
I would generate $cc$ and $ee$ together, and play with the $D$'s, i.e., $Y\to cc YD ee$, etc. This will be slightly more simple, though equivalent.