Can you sit down with your children once or twice a week and teach them, using authentic materials (such as the Catechism) about the nature of the Church, the liturgy, and the Eucharist? If you could do that, perhaps you could explain that you're going to Mass in order to be present at the perfect act of worship and to receive Jesus in Holy Communion, even though you disagree with some of the things that Father does and says. It's not an ideal situation, but it's better than not attending Mass.
Yes, that's one idea that I have been really thinking about doing. My kids are ages 9, 5, 2, and 3 months, so I've been thinking about getting some Baltimore Catechisms and going through them with my kids each week. Do you or anyone else have any other good suggests for resources I could use?
If I were you, I'd get both the original
Baltimore Catechism (Nos. 1-4) as well as the
Revised Baltimore Catechism, Nos. 2 (New St. Joseph, Fr. Bennet Kelly) and 3 (Fr. Connell Confraternity Edition). Personally, I think the
Revised Baltimore Catechism is better overall than the original, but the original also has some questions which are sadly not found in the Revised version (such as the necessity of prayer for salvation as well as describing the rosary and sacramentals in detail, among other things). In a way, then, the two versions complement one another.
When your children are older,
This is the Faith (Canon Francis Ripley) and
The Catechism Explained (Frs. Spirago & Clark) may be helpful tools for continuing their religious education. See also Fr. John Laux's (M.A.) series,
A Course in Religion (six books).