bleeding between periods, or "Spotting" is nothing to worry about & is totally NORMAL when you are on the pill.
The lower dose pills (mircette, alesse) are more likely to cause that breakthrough bleeding relative to higher doses of estorgen.
Normally you are supposed to wait 3 months for your body to adjust to the pill & the side effects (spotting, etc.) to go away. If you still have the problems after 3 months, you can try a stronger pill. A higher dose of estrogen is more likely to prevent that breakthrough bleeding.
BUT the higher dose of estrogen... well, we all know that's not a good thing. more weight gain, bloat, & for me more moodiness. I tried different pills & I just chose to deal with the spotting.
& yes, skipping the 'inert' pills - the week where you're supposed to get your period, is perfectly healthy & fine to do. I don't know that it will make her more likely to have breakthrough bleeding though.