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Much could be said, of course, and every situation is unique. Hopefully a healthy, loving compromise can be established—and if not, good luck.
In your situation, I would at least try to find a church that isn’t so bizarre, and be sure to have a patient, reasoned defense to anyone who asks for your beliefs to the contrary. In my experience, nondenominational churches tend to be fairly tame, but do your homework.
Hopefully your wife will appreciate the wisdom of healthy compromise, recognizing less harm will fall upon your children. Remember too, we all survived church.
Do all things with as much patience and love as possible. Remind yourself that God is ultimately in charge of winning over your wife and kids. Your job is to love them, protect them in love, but love them. If you don’t, your marriage will likely tank, and that would arguably be worse for everyone concerned.
It isn’t easy. So do your best to love well, offer smart and reasonable compromises when necessary, and trust in the Spirit of Yeshua to finish the drill.