|I think the most important thing in general is to use 1/4-1/2 (max) the recommended ammount of detergent. Unfortunately, there's no magic perfect solution because of different water and washers, so the wonder detergent for one person might not work for another.
Most people follow a routine that's a variant of pre-rinse no detergent, 1/4 or so detergent in hot wash. Some add an extra rinse, but if you're in the laundromat, those extras can probably get pretty pricey. So something to consider might be periodically doing an extra hot wash without detergent (i.e. one extra cycle once a month or whatever, which will probably be more effective at thorough rinsing anyway, using hot water rather than the cold in most rinse cycles).
In general, though, besides making sure that you aren't using too much detergent, something that some of us find helpful esp. with older kids is to rinse out night diapers. I don't use a wet pail (more like a soggy pail), but have found that getting that super strong urine diluted helps keep things smelling better. I'm not sure a true wet pail offers many advantages for you (esp. with transporting the diapers), but if doing a pre-rinse is not a feature you can select without getting into big money, maybe wet pailing would help (wondering if soaking in water and having the water changed out would help replace that pre-rinse)?