Mammograms are less successful on those with dense breast tissue, usually younger women, but some women maintain lovely dense breast tissue even after menopause. (All dense breast tissue means it it's primarily glandular tissue, not fat. As we age, and particularly after menopause, our glandular tissue decline and fat takes over. This can be why some women suddenly grow breasts after menopause).
When you have a mammogram, areas of concern such as calcification, fibroadenomas and other types of cysts and tumours all show up as white, as does dense tissue. So, trying to read white on white is really hard, something even the best radiographers have difficulty distinguishing between. This is why at one-stop clinics, they will do an ultra sound too.
It's decidedly likely that if neither your or your mother's lumps failed showed up for similar reason. I say this as I also had the same issue and every single lump - have had a dozen or so - I ever had were ones I found myself, not a single one showed up on a mammogram , but did on a ultrasound. Even so, with the ultrasound, it can be impossible to tell if a lump is benign or malignant. Again, I saw this because after an ultrasound, my consultant was pretty certain it was nothing when it transpires I did have cancer.
For a long time, mammograms were considered the best screening. Even now, it's still the one they start with. I think this is because of how easy they are to perform. An ultrasound is more specialised and can take longer. However, this, or rather the understanding of dense breast tissue is something the NHS are starting to consider to the degree that if you are found to have dense tissue, then it will be more likely that an ultrasound will be offered instead.
Presently, the NHS offer an MRI to those with a family history of breast cancer, especially those who carry gene mutations on BCRA1, BCRA2, PALb2 to name a few.
Ultimately, a mammogram is worth having. It takes 10 minutes, if that, once a year.