2

× 帰宅すれば、必ずお風呂に入りなさい。Why is this incorrect? Is it because it is non-volitional? takes out the decision aspect?

3

ば only works as action and consequence. A common example given is "if you drop a ball, it will fall". You can't put a command, volition, etc, after ば, but rather a sequence of events; the result (ball falling) after the action (dropping the ball). And ば doesn't have a meaning of "when" either, and even translating as "if" would not make for natural English either at times. Like この通りを行けば病院につく. Again, action and consequence; go down this path and you will arrive at the hospital.

3

When you get home, be absolutely sure to take a bath.
A : 帰宅すれば、必ずお風呂に入りなさい。
B : 帰宅したら、必ずお風呂に入りなさい。

Jisho.org defines them as:

すれば

Expression
1. if so; in that case; in that situation​

and

たら

Conjunction, Particle
1. indicates supposition; if ... then; when; after​
あ、とりあえず包帯{ほうたい}しているけど、もし煩{わずら}わしかったら、家{うち}に帰{かえ}ってからカットバンに代{か}えても大丈夫{だいじょうぶ}よ。
Ah, well I've bandaged it for the meantime but if that's awkward then it's fine to replace it with a plaster when you get home.

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