Padded shorts aren't actually that obvious under a pair of pants... I don't know how old your mom is, but if it was my mom I'd feel better knowing she had hip protection as well as tailbone.
BTW, I've posted it before, and I don't think that multi-sport and especially motorcross type padding is really suitable for skating. If you look at what you linked there's very little padding over the lower part of the tailbone, which is where a skater is more likely to fall, where the padding is on those is more like lower back protection. Likewise there is protection for the iliac crest on the pelvis (which is where you would hit falling off something like a bike or skateboard, but not necessarily how one falls on the ice), but no protection for the "hip" bones (the greater trochanter at the top of the femur) which is where a skater is more likely to impact than on the upper part of the pelvis. They offer adequate protection for a variety of sports, and for a younger/lighter skater they may in fact be enough, but don't offer enough padding in the places that matter... I know they wouldn't for me.
Where I tend to fall the most lately is actually on my "sit bones".. and I haven't found a practical way to pad that area that doesn't result in interfering with movement or just plain looking ridiculous.