At the time of the breakup AlphabetCereal gets a copy and AlphabetSoup gets a copy. If they care, make Soup and Cereal pledge to purge the Soup specific or the Cereal specific parts. Either way, ban the soup company from selling cereal by consent decree and vice versa.
Splitting the datacenters might be trickier, but worst case, operate them jointly for 12-18 months, and at the end, each datacenter and the contents thereof are the exclusive property of one or the other. Or enact a third company to own and operate the datacenter under FRAND terms.
The big question would be how you deal with shared infrastructure -- compute, data storage, logging, etc. Google has a significant amount of highly proprietary code in those areas which they're undoubtedly using within their ads product; it'd be tricky to figure out how to deal with that in a split.
They should have spun off DoubleClick for Publishers and other server/ad mediation into separate companies and is likely what will happen if the government is successful in their case.
It's generally acknowledged in technical circles that antitrust action is a highly effective way to break up a monorepo.