Wilderness: ferns are very absorbent. Native Americans used to line papoose boards with them. I've used them wwhile hiking.
Indoors:
For each member of the household, prepare 5 x 5 inch squares of absorbent cotton cloth, as from old t-shirts, etc. Try to set a color code for each person for sanitation control.
When you visit "the throne", there should be a bucket of soapy water with a little bleach in it handy. Do your thing, use your cloth, then soak it in the little bucket. It is a good idea for each person to have their own bucket, but with kids you might have to just have one for the family.
twice a day- morning and evening- rinse out the cloths (use rubber gloves) and drop them in the laundry.
You may want to have as many as a hundred squares per person in order to be sure you have enough if you do a laundry only once a month. Most people will only need to go three or four times a day but you never know....
This really isn't that radical. It is just a slight adjustment of the old-fashioned method of handling infants' diapers back in the old days....