Yes, the white stringy mucus stuff clinging to the stools is candida for sure. The reason it is on the outside of the stools is because the candida has colonized and covers the colon walls like carpet. It has mycelial roots that penetrates into the colon walls and so will not be excreted or flushed out by laxatives. Getting rid of it is a 2 stage process.
Stage 1: Go on a Sugar and starch free diet along with antifungals twice a day. Natural antifungals plus nystatin and fluconazole worked for me because I had a bad infection. This restricted diet is the hardest part but critical for success.
Stage 2: After 3 months on this regimen you need to add high potency probiotics (50 billion cfu once a day, but better yet, twice a day is recommended). Get a probiotic with high concentration of bifidobacteria. Ultimate Flora is a good brand.
When you start with the probiotics you need to also start taking a prebiotic. The two prebiotics that are safe and won't feed candida are: galactooligosaccharide (Galactomune is the brand name - take one scoop every 12 hours.) and lactulose. If you live in USA you can buy lactulose on eBay. Start taking one teaspoon every 8 hours and after 2 weeks take 2 teaspoons every 12 hours. The prebiotics will feed the probiotics and cause a favorable change in the colon environment that will disfavor candida and crowd it out.
You should feel healed after 2 months on stage 2 but beware: reverting back to a "normal" diet (with any Sugar or any grains) at this stage can and will bring back candida. I found I can eat some potatoes now because they contain "resistant starch" that feed the good gut microbes. I really don't plan on eating any added Sugar (fruit with no added sugar is still aways off in the future for me) or wheat at any time. Paleo diet has transformed my health and I realize how bad the "normal" American diet is on health and well-being. I can't give any hard and fast rule on re-introducing other foods back into the diet except to say you should go slow and cautious. If you have a setback, stop and eat what you know is safe. It might take 6 months on stage 2 before you can start re-introducing risky foods (starches) back into the diet. Even after experiencing full recovery, I would avoid added sugar, all grains and the only dairy to be consumed is plain sugar-free kefir.