In my opinion, you should feed your children at least an egg a day and you will be doing them a HUGE nutritive favor. Occasionally serving nitrate-free bacon will do no harm.
I say this because of scientific research. There is huge debate in the scientific and research communities about the role of fats in health, the role of cholesterol in heart disease and other ailments, and the relative value of dense carbohydrate consumption compared to other nutrients.
One person posted a link on About.com that suggests limiting yolks to 4 per week, but hard research tells a different story:
... no relationship between egg intake and coronary heart disease incidence was found. It is concluded that within the range of egg intake of this population differences in egg consumption were unrelated to blood cholesterol level or to coronary heart disease incidence.
I don't know the range of egg intake, but in 912 people you can bet some were avid egg eaters. Even if no one ate more than 4 eggs, there was no difference found at all, so where is the boundary edge where those bad-for-you eggs start to have any deleterious effect at all?
Very respected researchers are avidly speaking out against the idea that cholesterol causes disease. Cholesterol, Friend or Foe says:
In conclusion, cholesterol is one of the most important substances in the body. We cannot live without it, let alone function well. The pernicious diet-heart hypothesis has vilified this essential substance. Unfortunately, this hypothesis has served many commercial and political interests far too well, so they ensure its long survival. However, the life of the diet-heart hypothesis is coming to an end as we become aware that cholesterol has been mistakenly blamed for the crime just because it was found at the scene.
For some understanding of why "it is found at the scene:"
Our stress hormones are made out of cholesterol in the body. Stressful situations increase our blood cholesterol levels because cholesterol is being sent to the adrenal glands for stress hormone production. Apart from that, when we are under stress, a storm of free radicals and other damaging biochemical reactions occur in the blood. So the liver works hard to produce and send out as much cholesterol as possible to deal with the free radical attack. In situations like this, your blood cholesterol will test high. In short, when we have a high blood cholesterol level, it means that the body is dealing with some kind of damage. The last thing we should do is interfere with this process! When the damage has been dealt with, the blood cholesterol will naturally go down. If we have an ongoing disease in the body that constantly inflicts damage, then the blood cholesterol will be permanently high. So, when a doctor finds high cholesterol in a patient, what this doctor should do is to look for the reason. The doctor should ask, "What is damaging the body so that the liver has to produce all that cholesterol to deal with the damage?" Unfortunately, instead of this sensible procedure, our doctors are trained to attack the cholesterol.
The research I've done has led me to believe that eggs are good for you and that they are more full of nutrients than any fortified breakfast cereal. Fat in and of itself is not bad for you (though when rancid, oxidized or when containing bonds in the trans configuration instead of cis it surely is). While it has more calories per gram, it is also more satiating.
The nitrates or other preservatives in bacon certainly do speak out against its common use. There are uncured bacons available in some grocery stores (don't be fooled by "no nitrates except for those naturally occurring in celery powder and sea salt", as that's just a dishonest and sneaky way to get nitrates in the bacon under another name and deceive you, the consumer—manufacturers feed the celery nitrate water, then extract the nitrates back out, and they extract nitrates from seawater, so it's no different). But the fat in bacon is not inherently bad for you. Want to know more? Read The Skinny on Fats. You might also be interested in The Oiling of America.
Also, what the pigs you're eating are fed can make a big difference. Pigs raised on a traditional small-scale farm where they are given nutritious, non-toxic vegetarian foods are going to be a lot more supportive of your body's health than other alternatives. Pigs can eat all sorts of good food scraps from a farm (almost like a replacement compost pile). It's okay to feed them excess cow milk (from healthy cows) if it's also a dairy farm. If the pigs are raised on commercial feed-lots with too many animals in the same space, all indoors, on antibiotics, fed commercial, processed feed full of soy and other toxins, well, that meat is not going to be as good for you.
Folks, the lipid hypothesis—that consumption of fats and cholesterol raise cholesterol levels and that these both cause heart and other disease—while still the party line of the medical establishment, is under serious fire from many researchers out there.