SSPX school? I'm not sure how to answer that, but my first instinct is a no.
You can teach your own children too ya know, and still be doing a great service and giving glory to God. You can part-time tutor children at a parish school you deem as being of service to the Faith, and not have to be a full-time teacher in today's world where wages are silly low and costs to live are incredibly high. It's not "not trusting God" to go seek a paying job so you can support a family... that's just the way it is and God wants you to use your gifts , for His glory of course.
Although I may add that teaching doesn't require someone to be of incredibly high and saintly patience, as some may say. Just an interest in it and continued desire is enough I believe.