"will you be going home" vs. "will you go home"

Solution 1:

They mean essentially the same thing: Are you going home this summer? which is probably the most neutral form of this question.

However Will you go home this summer? might be seen as being curt and could imply that you wish for that person to leave. It could essentially be taken as Will you please go home this summer? but without the please.

Will you be going home this summer? is more inquisitive. It implies that you are merely curious about to their summer plans and you don't particularly care what the answer is.

If this is being addressed to a person that you do not wish to go home for summer you could try asking You aren't going home for summer, are you? which retains the overall neutral value but implies that you prefer for them not to leave.