If by external stent they mean internal/external, where the stent is a perforated tube in the duct with a tube that goes outside of the body, then I am surprised that that wasn't done before the internal stent. I had two internal/external stents (both ducts) for a while and was so happy to have them internalized. But I knew because the doc told me that they would get clogged and need to be cleaned occasionally. That's what I thought was happening a few weeks ago, but it turned out that the tumor had grown up past the steel stents and was crushing the duct above the stent. So now I have another internal/external stent. But enough about me.
The external part of the stent is a tube ending in a valve outside of the body. If there is blockage in the duct, a "bili-bag" much like a urine bag is attached to it to take the overflow.
The advantage to the tube is that the docs can insert a wire to manipulate the stent and can insert contrast dye to check to see how the duct is working, all without any sedation or pain, just a fluoroscope and a quick check and the doc has a full picture.
Disadvantages are many. The tube hurts and may make it hard to take a full breath. There is pain after the tube is put in that may be significant for a while - it certainly has been painful for me. The tube is held down by stitches which can pull out. It is difficult to take a shower because you need to waterproof the hole in your body and the dressing and tube coming out of it. You will need to flush the line with saline on a regular schedule, and also change the dressing. If a drain bag is needed, you need to incorporate the bag into your daily wearing apparel - usually the bag is warn hanging from the neck so that the drain point inside the bag is about nipple level or higher, so that the bag doesn't drain liquids from the intestines all the time. You will need to empty the bag (if you have to have one) and keep everything clean. The tube and stent will need to be replaced - how often depends on how often it gets clogged but every 8 weeks or so is probably a fair estimate.
Unfortunately, if your internal stent isn't working, the external tube is the only way to go. I can only offer my experience with this and hope your experience is positive. As always, please have your mom talk to her doctor about the effects of any procedure, get her to write her and your questions down before the visit, and go with her or have a friend go to have another set of ears to catch anything that mom might miss.
God bless and prayers for your mother,