Suggestions for training a high-anxiety Doxie-Pin, please?

My 10-month-old male miniature dachshund/miniature pinscher has so many behavioral issues that I'm overwhelmed & thinking of giving him away. He is mostly house-trained, but he has #2 accidents when left by himself for even a minute or two. For example, he and my female doxie were in the house together with us. I went to shower, and 5 minutes before I came out of the bathroom, my boyfriend went outside to do yard work. When I came out of the bathroom, my female was lying on my bed dozing, and the male was running around as he does a LOT. He left a pile on the carpet, and he'd JUST been outside. He'll not go to the bathroom all night, and is obviously holding it when he goes in the morning (FULL bladder). He's had three #2 accidents in vehicles. He shakes when we stop somewhere in the car. I'm not sure if that's anxiety or excitement. He digs & has caused a dead spot on the backyard lawn where he pulls up the grass by its roots. He jumps on people when they're standing, and he jumps into their laps without their permission when they are sitting. He is unpredictable about his reactions to being touched, and he's even bitten (not broken skin, but fairly forceful) when surprised by a touch. Yesterday, he ate a golf-ball sized hole in my boyfriend's truck seat. He's so loving & can be so sweet. I just don't know what to do for him to correct the unwanted behaviors. I've tried so many techniques, even looked up information on Cesar Milan's website. We've kenneled him; we've asserted ourselves as pack leaders; and we've rewarded good behavior like crazy. We've taught him to walk on a leash successfully, as he was spinning and dancing around on his back legs when we got him. He'll sit, down, stay, and spin on his back legs for a treat. Our female is wonderful, never has accidents, and does exactly what she's told. I don't know how to get him to stop going #2 in cars & when he's left alone for a few minutes (we take them everywhere). Does anyone have suggestions? I'm looking for ways to handle him personally. I really don't have the money for an expensive professional dog trainer.