One of the problems with using the broiler to brown the skin, is your chicken isn't equidistant from the broiler, so your breast will burn if the rest browns.
A few ways I've gone about ensuring properly crispy skin.
- Separate the skin from the meat prior to cooking. This will let more of the fat render out and allow the skin to dry out quicker. I actually put oil and spices underneath the skin to achieve this.
- Brown the chicken either before or after cooking it. If you have a cast iron skillet as in the picture there, that works really well. Cook the chicken to proper temp, get your skillet really, really hot add some oil when the oil starts to smoke, toss the chicken in (so you don't cook the actual meat much more).
- Buy a blowtorch (a proper one from the plumbing section of a hardware store). Cook chicken slowly to right temp and then blowtorch the skin. Serious suggestion... Alton Brown suggested it even in one of his podcasts. Also see here.
Edit: Something else to consider. You mention that your mother never had this problem. The chickens today might have more fat than the ones your mother used. The skin won't brown completely till the fat itself renders out. Giving it time to do that, separating the skin, and making sure the surface is really, really dry may help. You really want to reduce the amount of moisture that is on/around the skin.