My DS at that age was still soaking his pull-ups, his pjs, and all his bedding, often twice every night. The problem with pull ups for little boys is that they have erections during the night - the pull ups mean that their penis is then 'held' in the upright position, even after they have lost their erection, and therefore, urine shoots upwards, away from the padding in the pull up, soaking everything through.
We dealt with this in two steps (I was returning to full time work and wouldn't be able to manage the washing anymore). First, we stopped using pull ups and returned to nappies. This seemed to solve the problem of everything getting soaked and it greatly reduced the amount of washing, and the distress for DS, who was genuinely mortified at how wet his bed would be.
Then, during a school holiday, we rented an alarm, and I slept in his room for two weeks - not ideal, but it was worth the effort in the long run. Every time the alarm went off, he would be bundled out of bed and would be put in front of the toilet to finish his wee. It only took a week until he started getting himself up. The alarm was amazing, but it did take some adult intervention to get it to work properly as a solution. For many kids, they don't hear the alarm going off so the alarm doesn't 'work'. Of course, in our case it worked because I was hearing the alarm and would wake him. I know it sounds inconvenient, but it was the best thing we did. Glittertwins - hope this advice helps you, too.
DS was then dry almost every night - he is now 7 and doesn't need to get up in the night to use the toilet. However, just one caveat - there were a few wet beds after the success of the alarm. We finally figured out that these wet beds coincided with those nights when we had switched off every light in the house. DS, it turns out, is a little bit frightened of the dark, and would have an accident while trying to get his bravery together to make the trip to the toilet! We started leaving a light on every night for him, and we stopped all accidents from that point onwards.
So, lots of advice re: kid, but I'm afraid I don't have any tried and tested advice regarding your SIL. Perhaps, if she asks you what to do, you could turn the question around and ask her what she thinks might work for her little one? Maybe, she's not interested in you solving her problem, but just wants to talk about her difficulties? Maybe try some reflective answers. When she complains about wet beds and lack of continence, perhaps you could asking how this makes her feel or suggest that she might be feeling tired with all that extra washing? Let her talk it out and she'll probably come up with her own solution?
Hope it all works out for them both (and for you) :)