Here's my take:
Regardless of the other foods that are still in the diet, I'd pretty much always choose whichever fats and oils are more naturally occurring than not. That said, I'd ALWAYS choose butter over vegetable oil, lard over canola, and coconut oil over corn oil. Those tend to all be saturated but the idea that saturated fats are "bad" or unhealthy is really a misnomer. They're actually quite a bit healthier than unsaturated fats (when they're good sources, this doesn't mean trans-fats) since they don't oxidize as easily and have a better chance of being properly utilized in your body and not cause oxidative damage within. Remember, even saturated fats are not 100% saturated- they're going to be possibly 50% saturated and the rest are a mix of UNsaturated fats.
Check out my post on fats & oils here: http://www.balancedbites.com/2010/07/fats-which-to-eat-and-which-to-ditch.html
If your family is at a point where ADDING good foods is easier than removing the bad ones, getting them to supplement with fish oil will help some of the negative omega 6 fat intake from the grains, though it won't help heal their guts. This can be a sticking point for most people- maybe getting them to move to gluten-free grains can be step 1, then so on.
If you want/need more help, I'm always around :)
Diane Sanfilippo www.balancedbites.com | www.facebook.com/balancedbites BS, Certified Nutrition Educator, C.H.E.K. Holistic Lifestyle Coach San Francisco Nutritionist & Paleo Nutritionist serving the Bay Area and beyond via phone & Skype consultations.