Hi, 

It sounds like you are doing mostly everything right. We wouldn't recommend introducing lady beetles however, since they don't tend to consume that many different insect species. 

For the squash issues, you can refer to our Key to common squash problems page . A floating row cover of insect mesh can help greatly in the beginning of the season but will need to be removed as the plants start to flower so they can be pollinated. 

We have a webpage on Root Knot Nematodes that you can refer to as well. Adding the compost and beneficials should be helpful. If you are seemingly still having issues with it and using a different resistant variety isn't working, then you can have the plants tested. Have you confirmed it is nematodes? Could you send a photo for us to help diagnose? Unfortunately there isn't a great way to fix it if it is. You could test it by planting some carrots in a container with fresh potting mix and seeing if they grow normally before spending money on a plant test which could be around $50 or so. Our plant diagnostic lab is currently not testing material as we wait for a new director to be hired so Penn State, University of Delaware, or Virginia Tech are accepting plant materials for laboratory diagnosis. 

A photo of the peppers would also be helpful so we can suggest management. Could it be blossom end rot? You can visit our Peppers page for a list of common problems with links. 

If you haven't had your vegetable garden soil tested for a nutrient and pH analysis you could also have that done to rule out if the soil is lacking or low in anything that could be causing some of these issues. 

Feel free to attach any photos to this response. 

Emily