I totally feel your pain on this!
We had this problem with both of our kids for several months off and on (more on than off!) at some point between age 1 and 2, but they are quite regular now. Also, our pediatrician told us that it's not necessarily abnormal to go 3 or 4 days between BMs, but if it makes her uncomfortable is the bigger issue.
You mentioned the dietary remedies, but you didn't say how long you stuck with them. It will take several days for a dietary change to take effect, then you have to be consistent with it to maintain regularity. For my daughter, apple juice didn't do a thing, but we did add prune juice every other day, then avoided cheese, bananas, rice and applesauce. If you're giving a multivitamin, check the iron content. Just like the iron in an adult multi causes US to have "slow plumbing," it will do the same for kids. I would opt for a no-iron vitamin.
We also introduced a food supplement called glyconutrients. Within a month (maybe even 2 weeks) my son went from screaming and crying through a BM to not even noticing them. We started them sometime soon after his first birthday. As his diet increased in variety, the problem came back somewhat, but we have added a cup of apple juice (full strength) to his diet daily. Until recently (he just turned 2), if we ran out of either juice or glyconutrients he'd have trouble. Now he seems a little less reactive, though we can't get within 20 feet of a banana without major problems in this area.
When things got bad with him, milk of magnesia worked (sometimes in 2 hours, sometimes in 24 hours)
Also, babies/toddlers won't be able to differentiate between pain caused by a large BM and pain/cramping caused by the act of passing it. If the contents of her diaper don't seem large enough to warrant the fuss caused by passing it, you might be dealing with lactose intolerance. Maybe switch to lactose-free cow's milk for a couple weeks and see if she improves.
Yes, there are prescriptions to treat this, and certainly use them if it gets bad, but in the end you're treating a symptom and not dealing with the problem that caused it. I would stick with dietary management, and be careful not to try too many things at once. Make one change and see it through for at least a week before doing anything else. If a remedy works, stick with it permanently.