Yes, this is a much harder challenge than I face, because you have the responsibilities of a father. Husband and wife are supposed to be united, but your wife is not in harmony with the Church’s teachings and your children need to know and embrace the full truth of the Catholic Church. So your duty to be a spiritual leader to your family and instruct your daughters so that they don’t become Cafeteria Catholics puts you in a very painful position. There are no easy answers to it. One just has to stand by one’s principles and speak the truth with whatever grace one can.
That’s a good idea. It’s an extremely hard place you’re at. Your purpose is righteous. Relying on prayer is crucial. Do you think she would be willing to accept establishing a family prayer time once a week on Sundays? The family reading a Bible passage and praying together out loud, thanksgivings, petitions and anything else, for perhaps 15-20 minutes might create certain bonds of faith and unity outside of the family disagreements over doctrine.
Researching all the points of doctrinal disagreement online can give you the knowledge base you need to answer any objection or conflict your wife has. The Catholic Church, as you know, has very good answers to your wife’s errors, and knowing those answers is crucial to being able to help your wife understand them. After you learn the answers, you don’t need to make her hear them. You can just wait for a time to come up when in natural conversation an area of dispute comes up, and then you’ll have the answer and can bring it to her.
Doing research is very valuable for preparation.
Prayer is essential, too. A lot of personal, steady prayer for their conversion, especially praying to our Blessed Mother. Praying for humility is wonderful too, for this makes your prayers more acceptable to God and makes Him able to work through you more perfectly. Prayer is my greatest weapon by far in bringing my family toward the faith. I’ve done a lot of research too, so I have a well researched answer whenever they have a question. But your wife will bring her questions to you in response to the Spirit’s working on her heart. It doesn’t have to be you pushing things on her that she can’t accept. Pray for her to Mary, steadily and systematically, and wait for the fruits to take shape.
When a situation comes up in ordinary conversation where a topic of faith arises, in her presence or your daughters’ company, then let the truth be known if the time seems appropriate to you. If you feel your daughters have received false information but the time isn’t immediately appropriate to correct them, then wait for a while and do it afterward. That’s what I did when my brother David was receiving baptismal instruction. He received instruction from a Protestant pastor about how baptism is symbol alone, and I didn’t dispute him then even though I badly wanted to, because given the setting and time, it wouldn’t have been appropriate. Therefore I waited and after the pastor had finished and left the house, I presented my brother the truth.
Show grace, tact and love, and don’t feel like you have to shove the truth down the throat of anyone opposed to it. At the same time, don’t hide the truth, though. Be bold and give your opinion when you feel it is appropriate and useful.