How Can I Help My Dog?

I recently adopted a 2yo mutt from a shelter. She came home perfect, housebroken, etc. In the last few weeks she has started peeing at night (while I'm asleep, always in the kitchen), and peeing and pooping sometimes while I'm gone. I started clicker training w/ her but she doesn't seem to "get it." I used cheese and liver and she stared at the treats without fail but wouldn't respond to me clicking for the behaviors. Every time I try to do anything with her, she rolls onto her back, if I sit on the floor she gets on my lap, if I pet her she follows my hand away and mugs it with her nose or jumps on me. She had begging issues at first but now knows she won't get my food. These are certainly small things, esp for a rescue dog, but I work in a job that I have people over to my house a lot and I can't have her in my face or their face. My feeling is that after her rescue from the shelter, her 'foster family' spoiled her rotten. I simply cannot have a dog that I can't train, I'm at my wit's end. Help?