Yeah in the beginning she mentioned that she didn't get anything of the money because her mother spent it all on lawrence before she was of age. If she get's married then she becomes head of the rozan house since since she was the last heir anyways it just sped up the process. The mother doesn't care for tia at all and believes that all of their possessions should belong naturally to lawrence (i mean have you seen the way she treats him in comparison to her brother. way to plant all your eggs in one basket) I felt really bad for her in her past life. at least now she can live well in this run since she knows what's up. (I mean she literally was one with all the brains in the family it was just that family full of pig team mates that betrayed her.
Why is she so fixated on keeping Tia by her and Lawrence side when she treats her so terribly? Is it for the estate and money? Because, If Tia gets married would her husband have control of it all. Considering Lawrence is the Emperor's son and not Marquis Rosan's, he won't get anything. Tia is the only reason they live so well, the Emperor isn't putting in any effort to support them.