This is what canon law says (among other things):
Can. 798 Parents are to entrust their children to those schools which provide a Catholic education. If they are unable to do this, they are obliged to take care that suitable Catholic education is provided for their children outside the schools.
and also
Can. 803 §1. A Catholic school is understood as one which a competent ecclesiastical authority or a public ecclesiastical juridic person directs or which ecclesiastical authority recognizes as such through a written document.
§2. The instruction and education in a Catholic school must be grounded in the principles of Catholic doctrine; teachers are to be outstanding in correct doctrine and integrity of life.
§3. Even if it is in fact Catholic, no school is to bear the name Catholic school without the consent of competent ecclesiastical authority.
If you are unable, you are unable; you do not need to impoverish your family to make tuition to a school that is beyond your means. If the Catholic schools available to you are affordable but, unfortunately are not only but nominally Catholic but in fact pose a danger of undermining your child’s formation as a Catholic, then it would be fair to conclude that those schools, in spite of their stated reason for existence, do not “provide a Catholic education”, and therefore must, in good conscience, be avoided.
If a Catholic school is available to which you cannot object to on the terms above, then as canon law reads, you ought to send your children there. What “object to on those terms” means is something for the parents to discern, however. I am not proposing to be an expert on where the boundaries are, only to point out that the boundaries are there in canon law to be taken into account:
vatican.va/archive/ENG1104/__P2N.HTM
PS Homeschooling, if done according to the directions of the parents’ bishop, would qualify as a Catholic school. If the bishop says, “this is a Catholic school”, then it is a Catholic school, even if school is conducted at the parents’ kitchen table. The parents do have a responsibility to ensure that the education they are providing at home has the consent of the competent ecclesiastical authority, however.