Eudoria's plans are deliberately obfuscated to allow for sequels
Director Harry Bradbeer told the Decider website that Eudoria's actions and plans will be revealed in sequels.
DECIDER: This is a mild spoiler, but we didn’t quite find out what Enola’s mother, played by Helena Bonham Carter, was up to in the end. What can you say about that?
BRADBEER: I can say it will certainly be looked into in future movies. And I’m delighted to say I’m not entirely sure what she’s up to.
BRADBEER: Not all the details. I know quite a bit, which I can’t divulge. But I’m excited about the other things that she’s going to do. She’s such an extraordinary character that we’re going to dig out some more secrets about her. If we do go again, there’s a lot of issues left in this dysfunctional family. Not only in the country, which is dysfunctional, but the family as well. I think it will always be leaning into real historical accuracy, about the history of the constitution and the development of our democracy. And of human rights, not just women’s rights. I think that’s a very ripe scene to plow. Because if you have an adventure film that has something interesting to say morally, I think that really enriches it and makes it more nutritious.
Eudoria was planning some sort of radical action with the Suffragists
We do know that Eudoria left Enola behind for her own safety to commence some radical and underground action with the Suffragists. This may have been headed off by the indirect consequences of Enola's actions.
Her saving of Tewkesbury led to the unexpected success of the vote in the House of Lords to allow more people to participate in democracy; and her destruction of the munitions / fireworks may have headed off an explosive demonstration of the Suffragist movement's power when (as expected) reform in the Lords failed.
Eudoria's clues and money were a device to tempt Enola into leaving the nest
'She wanted me to find my freedom, my future, my purpose.'
To achieve this Eudoria resources Enola and tempts her with the idea of finding her mother. She has no intention of actually allowing Enola (or Sherlock) to find her, but this is the only device that will pull Enola into independent action and to start to realize her calling.