Well I think that you've answered your own question, you can improve the quality of fat that they eat, but you shouldn't try to add additional fat to their diet.

I think that a low-fat/high-carb diet is a much better choice than a high-carb/high-fat diet, which is the worst of all worlds. Whether you believe in the insulin-hypothesis or not, adding extra calories to your diet is rarely going to be a good idea.

Here's your answer:

"But then again, coconut oil and other good sources of fat have to be better than using stuff like...Pam or "I Can't Believe It's Not Butter" (shudder)..

I think borofergie's on to something, though. My suggestion would be to use "real fats" and real food for whatever your mother cooks for the family. (In other words, eggs instead of Egg Beaters, put butter in the pan instead of Pam. Maybe even switch to 2% or whole milk if they've been using skim.) Will it be some more calories? Yes. But who's to say they won't eat less overall, since they might be a little more satisfied by eating foods the human body actually recognizes?

I wouldn't intentionally add fat to things on top of a SAD; just replace the industrial/crap fats with good ones. (And maybe even some nights, your mother could "forget" to cook pasta and everyone could just have double helpings of vegetables.)

Bottom line: err on the side of real food!

Any improvement in the quality of food is good. Think about it- you put, say 240 calories worth of coconut oil into something that they eat. This means they will likely eat 240 calories less of some crap. In addition, they've just got some healthy saturated fat that they would have never gotten otherwise. Coconut oil in particular is much praised in various corners because helps with energy, weight loss, the ability to think, etc... People are even using it to combat Alzheimer's.
But this would be true about most saturated fats. If they are simply eating out of control and gaining weight rapidly, it won't be because of the healthy fats you add to their diet. It will be because of the highly processed carb and pufa laden junk that they eat.

Franken-fats (canola oil, margarine, etc...) have the same amount of calories as natural fats (coconut oil, butter, olive oil, etc...), so swapping one out for the other won't add any calories to anyone's diet.

IMHO, you can't win a war with relatives about paleo/carbs (people either buy into it or they don't), but there is a way you can phrase your position that will allow you to win the early battles:

Processed foods

Almost nobody agrees that processed foods are good for you. If you say that, for health reasons, you want to reduce the amount of processed foods and eat more whole/natural foods, your relatives will have a hard time arguing with you.

You can say you want to eliminate the laboratory created fats like margarine, canola oil, and corn oil and and go with natural fats (butter, olive oil, etc...)

You can say you want to eliminate laboratory created sweeteners like high fructose corn syrup and replace them with natural sweeteners like honey and cane sugar. Of course, almost no products are made with honey or real cane sugar anymore (even loaf bread and pasta contains high fructose corn syrup) which gives you an excuse to eliminate those products (or at least greatly reduce them).

You can use trans-fats to back up your position that you want to eliminate laboratory created foods. For decades margarine was pushed as being a healthier alternative to butter, only later did we find out that margarine contained trans-fats--a substance that is now universally understood to be incredibly dangerous to your health. Do other laboratory created foods (like canola oil) contain the next "trans-fat?" Nobody knows for sure, but given the track record of laboratory created processed foods, you can make the case that it is healthier to go with natural foods.

Even if your family ends up incorporating natural carbs (rice, potatoes, yams, etc...) they'll be better off. The majority of people's carbs come for processed foods. Just by eliminating processed foods you're getting your family 90% of the way home.