-I'm not an expert, but have grown raspberries for a number of years and had excellent rewards. (I love the berries, juiced...it's to die for! And, I also freeze them, mashed, then when ready to use, sweeten and put on my freezer waffles. Yum!)
OK, first, your problem may be that you're mixing blacks with reds...that is a no-no. I have literature that recommends keeping a distance of at least 100 feet between the two varieties. ( I grow purples, and that rule is the same for them, tho I don't have quite that much room to grow them that far apart, and so far, they've done quite well, but I do keep them at a pretty good distance.)
The next question would be.....are your reds the summer or fall bearing varieties, since that does make a difference in when and how to prune them. I have always grown the summer bearing ones. With them, in the fall, after they have borne fruit, you should cut (not pull!) those dried out canes (you can tell the difference) down to the ground and dispose them....to prevent disease. If you pull them out, you will pull out the new canes that have grown from that root, and lose those berries for the next year.
It really does help if you can apply manure (I can't), but I do fertilize twice a year, and I just happen to like using Jung's raspberry fertilizer, since it's easy to use..just mix with water and put in a sprinkler and apply, going down the rows. (The pkg. gives the directions. And, I have no relationship with the nursery, other than liking them.)
If you can mulch them, all the better....leaves are great...that is what I use, having a big English walnut tree that gives me a huge supply! My book on berries says your harvest will be bigger, if you mulch with leaves.
In the early spring, you will need to prune back the now tall canes...I cut them back to about 5' or a tad more. I also keep my rows confined with stakes which I put heavy twine all along the row...that also holds up some of the floppier canes.
I repeat...I'm no expert, but if you have mixed the reds and blacks, my guess is that you should dig them all up and plant from a new source of the one variety you prefer to keep, a distance away, probably not that far, since your "contaminated" sources will be gone. (Unless you have a very large lot, and can plant both varieties, only a safe distance from each other.)
One last thot...if you have the fall bearing reds, their pruning is different. I just planted some, and have not learned what their procedure is, but if you tell us that is the kind of reds you have, one of us will check our directions and give them to you. I recall that the pruning is different. The rest of the directions would be the same...distance from blacks, mulching, and fertilizing.