It wasn't planned that way, but the hookers admitted they were invited to Atlantic City to sleep with voters to change the voters' minds about candidates. That admission (that they crossed state lines - from Pennsylvania to New Jersey - for immoral purposes meant they were breaking a federal law (The Mann Act). Nucky's lawyer knew that if Nucky was charged with a federal crime then Nucky could ask his friend in the White House for help, and that help would probably get the charges dropped.

Nucky is quite smart, but also quite lucky. It was Nucky's luck that the Commodore had a stroke (and without the Commodore being active, the others against Nucky stood no chance of beating him).