I've been thinking about this for quite awhile now... (which I'm sure some of you have as well) ... Is Big Mom actually the Alliance's target? It is only natural for people to believe they are undoubtedly after Big Mom, granted that Luffy accepted Law's proposal it shortly after he personally declared war with her:
But if you think about it, Luffy does have motives to take down other Yonkous as well:
Blackbeard: Ultimately, he is responsible for Ace's death. He is arguably the root of all of the issues the OPverse faces today.
And just look at how much Luffy hates him, that glare of hate he give BB. (after realizing that BB is the reason why Ace was put in Impel Down in the first place)
Shanks: Yes, Shanks. The inspiration, the reason why Luffy became a pirate. Luffy's role model.
I recall reading a different translation, and watching the Anime version of this page in particular. Luffy swears that he will someday gather a crew that will beat Shank's crew. In other words, he won't lose to Shanks. What better way to surpass your role model than to defeat him in combat? It's not like he wants to kill him or dethrone Shanks or anything, he just wants to prove his worth.
Kaidou: We've yet to be introduced to Kaidou. But, given that there was no clear indication as to which Yonkou the Alliance is after:
It is still OPEN TO INTERPRETATION as to which Yonkou the Alliance are planning to take down.
I'm not saying that Big Mom ISN'T the prime target, however I am saying that there isn't enough concrete evidence that indicates that she is.