I feel for you. We live here in Mexico, living part time in a more central place and part time in pretty remote village. (We got electricity there about 3 years ago). Especially when we're in the village we've experienced what you're describing.
I'm pretty sure it is amebas, it could also be a bacterial infection - Shigella, but the onset of Shigella is usually more sudden and with fever.
Is there any lab nearby where you could take a stool sample? That way you would for sure know what it is.
If it is amebas, I'm sorry to say that for us, we usually had to take Flagyl finally if we had it really badly, because the other things didn't help. But I do know that for some people other things help, so I'll mention them here.
Grapefruit seed extract
Papaya seeds, ground, one tablespoon three times a day for seven days (I'm not sure if you can get you're little ones to swallow that one, maybe with a lot of jam around, I can hardly swallow it.
What I like to take are strong probiotics, but I think they are better at the beginning or for prevention (those who aren't sick yet), I'm sure they are still helpful to take later, but can't win the battle by themselves.
I also have a book called "Natural Medicine in the Tropics" Here's what I found (don't know why we never tried that
* Chop garlic into very small pieces and take 1 big spoonful together with some tea 3 times daily for 5 days.
* Mango leaves - take 1 handful of fresh young green leaves, boil with 1 litre (that's about 1 quart) of water for 30 minutes, filter and drink in portions during the day. Combine with asthma weed (if you know what it is, I don't), for greater effectiveness.
* Guava, for light cases: take one handful of guava leaves (i.e. the amount the patient can hold, or hide, in his or her fist) and add one litre of water. Boil for 20 min. in a covered pot, and then filter. Add more water to bring the volume up to 1 litre again. Drink in portions through the day.
- for serious cases, make a tea combined with other plants (see above).
So, I hope some of this is helpful, and you're getting over it soon.