I always soaked mine in a bucket with water and tea tree oil until it was time to wash them. If the diapers had solid waste, I dumped it in the toilet; if it was especially icky I would rinse it off before adding it to the bucket. If you have trouble getting your detergent to dissolve, put it in a bit of hot water to do so before adding adding it to the dispenser. Or even add it to your washer as the water is filling up before adding your diapers. I know this isn't possible if you have a front load which is why you may have to dissolve it before adding. My front load has that problem with some powders so I just dissolve it first. Unless there were a lot of poopy diapers in a load, I never rinsed them first, and I would wash with hot on all of them (I had a very eclectic collection and I did not have the time to sort through them; I never ruined any diapers unless I forgot one in it's plastic baggie under a seat in the van or something.)
Why are you drying the inserts etc. on low? Especially if you know you'll just have to put them back in. You could certainly hang dry the inserts. You could even put them in on low a bit but instead of putting them back in the dryer, hang them up then. Since your stash is small, the biggest thing you have to do now is to get into a routine so you could hang dry all of your stuff but still have nice dry clean dipes for her when you need them. Yes, it is entirely possible. A friend of mine doesn't have a dryer and she has to hang dry everything; she has two little ones in diapers. She figured out how long it takes for the stuff to dry, how many dipes she needed a day (throwing in a few extras for unexpected stuff), how many cloth wipes and she went from there. It is easier when you have a bigger stash going but still possible with a small one. Until you do, if you want to hang, you will have to do her soiled diapers every day. In my routine (hanging outside in the summer and sometimes inside) I had to do mine every 2 days.
I didn't really care about the stains but I also rarely had them. The sun does take care of a lot. Country Save has a powdered bleach that I sometimes use if I feel the need.
This link has some info you may like. It's the same site I sent to my sis when her baby was born and she was asking questions (and too impatient to really listen to me. ) http://www.diaperpin.com/howto.asp