Answer
See the detailed answer below.
Work Step by Step
We have here 4 frames of reference, $\rm S, S', S'', S'''$ for Earth, and the three spaceships respectively.
Where
$$v_{\rm S'}=v_1=0.3 c,\;\;\;v_{\rm S''}=v_2=0.5 c,\;\;\;v_{\rm S'''}=v_3=0.7c$$
Let's assume that the origins of the 4 frames are at the same point at $t_D=0$, so
$$t_D=t'_D=t''_D=t'''_D=0$$
And
$$t_E=1\;\rm y$$
$$x_E=2\;\rm ly$$
$$\color{blue}{\bf [a,b,c]}$$
Now we can use the Lorentz transformation to find the time at which Epsilon exploded.
$$t'_E=\gamma\left[t_E-\dfrac{v_1x_E}{c^2}\right]$$
where $\gamma=\left[1-\frac{v^2}{c^2}\right]^{-1/2}$;
$$t'_E=\left[1-\frac{v_1^2}{c^2}\right]^{-1/2}\left[t_E-\dfrac{v_1x_E}{c^2}\right]$$
Plug the known;
$$t'_E=\left[1-\frac{0.3^2c^2}{c^2}\right]^{-1/2}\left[1{\;\rm y}-\dfrac{0.3 \left(\frac{1\;\rm ly}{\;\rm y}\right)(2\;\rm ly)}{\left(\frac{1\;\rm ly}{\;\rm y}\right)^2}\right]$$
$$t'_E=\color{red}{\bf 0.4193}\;\rm y$$
So, for $\rm S'$, there is a time difference between the two events about 0.42 years.
By the same approach,
$$t''_E=\left[1-\frac{0.5^2c^2}{c^2}\right]^{-1/2}\left[1{\;\rm y}-\dfrac{0.5 \left(\frac{1\;\rm ly}{\;\rm y}\right)(2\;\rm ly)}{\left(\frac{1\;\rm ly}{\;\rm y}\right)^2}\right]$$
$$t'_E=\color{red}{\bf 0}\;\rm y$$
So, for $\rm S''$, there is no time difference between the two events which means that the two events occurred simultaneously.
By the same approach,
$$t'''_E=\left[1-\frac{0.7^2c^2}{c^2}\right]^{-1/2}\left[1{\;\rm y}-\dfrac{0.7 \left(\frac{1\;\rm ly}{\;\rm y}\right)(2\;\rm ly)}{\left(\frac{1\;\rm ly}{\;\rm y}\right)^2}\right]$$
$$t'_E=\color{red}{\bf -0.56}\;\rm y$$
So, for $\rm S'''$, there is a time difference between the two events of about -0.56 years, which means that the Epsilon explodes before Delta.
$$\color{blue}{\bf [d]}$$
The two events are independent since the light explosion of Delta would reach Epsilon after two years while the Epsilon exploded just one year after the explosion of Delta.
So there is no causality violation, and it is normal, in some reference frames, that one event occurred before the other.
