It takes real effort and a willingness to be creative, but it is absolutely doable and worth fighting for if that is what you want.
On the marriage side, communication is everything. Write letters, real ones, not just updates about the bills and the kids. Write about the future you are planning together. Write the kind of letters that remind both of you why this is worth holding onto. Intimacy does not have to disappear because he is inside. Sexy letters, inside jokes, shared memories, plans for when he gets home, all of it keeps the emotional and romantic connection alive in a way that a five minute phone call cannot. InmateAid makes it easy to send letters and photos regularly without the hassle of printing and mailing yourself, which removes one more barrier to staying consistent.
On the kids, the framing matters more than most parents realize. Children take their emotional cues from the adults around them. If mom is devastated and ashamed, the kids feel that and internalize it. If mom treats visits as something to look forward to, as a chance to see dad and show him how much they have grown, the kids carry that instead. Make the visits an event. Let them draw pictures to bring. Have them help pick out photos to send. Build anticipation around letters arriving from dad.
It is not going to be easy and anyone who tells you otherwise has not lived it. But plenty of families have come through an incarceration stronger than they went in, because the distance forced a level of honesty and intentionality that busy everyday life never required. You clearly want to keep things together. That desire is the hardest part, and you already have it.