You might consider that she is experiencing difficulties not because the formal proofs per see are difficult, but because she has not developed intuitions about mathematics. Starting a mathematical education with a focus on set theory leads to a situation where the student is spending most of the time making a colossal effort to prove in a very abstract way something that seems trivial while not knowing why. The New Math movement in the US failed drastically in this approach.
Supposing that understanding maths is synonymous with being able to talk to mathematicians and understand why they are interested in a given topic, I think it is important to try not only to grasp formal proofs, but to understand that they are necessary because our regular intuition fails to consider interesting structures that are logically possible.
Given all I said, I would suggest going back to geometry. It is a topic where everybody has some intuition about the objects involved and at the same time has plenty of interesting constructions that help motivate the need for proofs. One suggestion would be to use A. P. Kiselev's two volumes "Geometry". This is a soviet textbook for advanced high school, and has a very professional "proposition-proof" style for euclidean geometry, while trying to introduce more advanced topics, for instance the first book, on plane geometry, will introduce the concept of homothety and similarity transformations (which should help her have a first contact with the notion of a group and a higher level of abstraction) and the second book, on solid geometry, finishes by introducing vectors and having a first discussion on the foundations of geometry.
A follow-up could be Coxeter's "Introduction to Geometry", a book aimed at undergrads. It is divided in four parts, euclidean geometry, coordinate geometry, foundations and differential geometry. It is not meant to be thorough but to give an introduction to interesting problems in each of these parts of geometry. It has a lot of discussion on symmetry groups and non-euclidean geometry.
I must say I'm biased in liking a lot of group theory, but maybe she could profit from this kind of focus. Studying geometry from the ground up with a focus on symmetry is a way of using an intuitive topic, with plenty of room to pick up basic competencies (such as elementary algebra) and introducing a topic that motivates more abstract reasoning (from the symmetries themselves to the abstract concept of group grounded in set theory and algebraic structures). It also has the benefit of leading straight to a discussion of the Erlangen program and a discussion of the foundations of geometry (and maths), something a philosopher might find interesting.
Since you mentioned complex numbers, in the same vein I would recommend I. M. Yaglom's "Complex Numbers in Geometry", another soviet book for advanced high school. It requires being comfortable with elementary algebra, but introduces complex numbers with a focus on transformations on the plane. It also introduces dual numbers, which I find neat at this level to look at the myriad of interesting objects that are logically plausible, and motivate more abstract reasoning about structures.