This situation bugs me to pieces what should I do?

Been married for almost a year. We have been bickering and argueing for quite some time now. The majority of our arguments and problems basically have to do w/trust issues on my part. It seems as though every time we have a problem he goes to his parents about it and it upsets me. I see our problems as something that is very personal and shameful to me. I'm ashamed of not being able to trust him and at times I do admit our arguments are petty. His parents are very kind people and I hate that he goes and basically "cries" to them about our stupidness and makes me look bad. They dont get to hear my side of the story! Not to mention we both have a temper! Now, my MIL wont talk to me. We work in the same place and she avoids me at all costs, not only that but she never calls me like she used to anymore and everytime I am around her she ALWAYS talks about her other daughter in law. I dont know if she does it purposely but its obvious there is favoritism between us. I hate it. I hate the thought of "talking to her about it", seeing as how there is so much pettiness going on, talking to her about it seems worse. I have talked to my husband about not going to his parents w/every little thing and all he says is "Ok I understand..." but the next argument, there he is calling them. What should I do?