Ceremony with no wedding party on bride, groom and kids

I think it would be nice if your officiant said something about how this wedding is special not only because of the binding of two people in love, but that that love also brings the unity of two families. Then you can have the kids come up to do the sand binding

Agreed. I would ask the officiant to call the kids up together to stand with the two of you, then talk about how the wedding is uniting a family, then do the sand ceremony. A gf asked me to officiate her Quaker/self-uniting ceremony some years ago and we wrote the transition as simply, "To celebrate their new family, Name and Name would like to invite their daughter Name up to join them here and hold their hands." Then I said something similar to what JA suggested.

It was a natural and happy accident that my friend pulled her teen daughter up to stand between her and hubby, and they each crossed their arms behind the daughter's back, which created a nice photo opportunity. What a beautiful idea to adapt the sand ceremony to include your whole family!