Why is the series called "Amaama to Inazuma"?
One interpretation of the title can be:

甘々ちゃんといなくなった妻 

[稲妻]{いなつま} is basically a play on words for いなくなった妻, more or less "the wife that's no longer there". Implying that someone is widowed.  

甘々ちゃん however is a bit more complex. 

It can be interpreted as 甘な甘ちゃん. The expression here is a bit multifaceted, so I will try to break it down. 

While 甘い does mean sweet, but it has other meaning out side of food. When used to describe a person, it can also mean naive. 

Someone who is referred to as an 甘ちゃん can be described as a "soft" or "naive" person. Adding 甘い to describe someone who is an 甘ちゃん reinforces the naive stereotype. The nuiance here is a bit negative,implying that this person is a clueless (naive) idiot.

One can imply that the title refers to Inuzuma-sensei, being a very soft spoken, yet clueless single parent raising a daughter, who not only doesn't know how to cook, but doesn't know to to take care of Tsumugi (in place of his late wife). 

You could imply that the alternate meaning to "sweetness and lighting" to be "the naive widow".  



However, if you refer to the author's afterword in vol.1 of the manga, 



Despite many alternate interpretations of the title, the title is intended to be something warm and fuzzy that appeals to the 5 senses, nothing more than that.