Lots of possibilities here. Not sure how likely any of them are though. The navy was already getting tired of Babbage at this point. Maybe Lovelace could have convinced him to sit down and just finish one of his machines for once. The British navy with better tide charts and artillery tables would be even more impressive, but militarily wouldnt play a huge role unless the splendid isolation got butterflied away. Which could happen, but commerce is what the Empire really cared about. And on that front the engine could have started the automation of shipping ledgers, inventory and maybe even taxation almost a century early.
Culturally the impact is potentially even more interesting. If computer programming is seen from the very beginning as a female job, like nurses or telephone switchboard operators, then verious organization might hire women as the 'natural' operators, maybe even on board ships in the navy if they come with difference engines, which they might by WW1. And, when the home computer roles around it is seen as the domain of the woman of the house. All of online geek and nerd culture could start with a heavy female bias. "There are no men on the Internet."
Each step is a bit of a stretch though.