Loose stools are common with intolerances but that's not the only way they present - any gut/tummy/intestinal "differences" might also be related, so constipation *can* be as well.
I would be very leery of introducing soy as a dairy replacement; the proteins of soy and milk are apparently similar enough that people who have a problem with one often have problems with the other. My family can only do trace soy; J used to have soy milk before I knew better and WOW, some major poop issues ensued.
We can now have yogurt (cultured dairy seems to be OK for us now, as the culturing apparently "pre-digests" some of the protein and sugar to make it easier for us to handle), but otherwise we avoid dairy and most common substitutions like soy milk. I make a wicked coconut milk breakfast smoothie, and Natalie does drink some rice milk (I try to limit quantities after finding out that rice has naturally-occurring arsenic in it - it draws it from the soil it grows in, apparently), but mostly we drink water, not even juice (fructose is another problem for us). I'm allergic to almond milk, so I just don't bother getting it because I'll have some of the rice milk once in a while to thin a smoothie.
Since you mentioned behavior and antibiotics, I always attach this for reading up on gut health and behavior:
http://www.diannecraft.org/article-001.htm. Are you all on probiotics? Definitely recommend!
And as for wheat, wow, on the one day a week my kids still get PBJ's (peanut butter and jelly sandwiches) for their school lunches, I can see a behavior and mood difference for sure. School year's almost over, and starting this summer when there's more time (kids home to help, plus I'm a teacher so will be off myself) I want to do some coconut flour bread and tortillas to use for stuff like that. There are a LOT of gluten-free recipes out there, but as I'm allergic to almond flour, which is a staple of many of those recipes, we just don't bother unless it's coconut flour. I have had to relax on my Paleo thing lately as an injury has sidelined my physically, so I'm relying on stuff I wouldn't normally feed my kids the last couple weeks in particular.
One more link to check out from a blog I follow, Paleo Parents. Here's their Before and After story, which talks about the changes the whole family went through. On days when I wonder why the HELL I undertook such a big change (which I don't regret unless I let it all pile up LOL), this makes good inspirational reading:
http://paleoparents.com/our-before-after-story/