IMO you, your mom and your sister are a real asset to the show. The three of you provide an example of respect for yourselves and for others. You add a natural air of style and class to RHOA as opposed to the more ostentatious persona of some of the other cast members.
That said, what really drove me to this blog is the animus your husband feels toward your sister. Needless to say you are a grown woman capable of making your own choices. In this instance however your choice affects not only you but also the rest of your family.
I understand the skepticism your mom and your sister feel about Peter. After watching him on the show he strikes me as insecure in your relationship and often times presenting an ugly macho man front to mask that insecurity IMO. It seems as though Peter has a problem reflected in behavior that is at times uncouth, immature and totally inappropriate (particularly for a grown man). Starting a fight with Apollo at Kim's baby shower, a no show for the opening of the Bailey Agency, making gratuitous disparaging remarks about Sheree and Phaedra during an interview, publicly embarrassing your sister at the anniversary party and that crass no class whistling to announce your entrance at the party -- all unacceptable. Glossing over bad behavior or excusing it because he was in a "mood" is a bad sign and a red flag in your relationship.
When there is a history of love, trust and support from your immediate family don't ever allow boyfriends, husbands, affiliations of any kind to damage that family relationship. It's a red flag when your boyfriend, husband or whomever is willing or desirous of damaging that relationship. The husband who really loves you would respond to such a rift by recognizing that your sister loves you, you love your sister, that relationship is important to you so you all need to do whatever is necessary to work it. They don't respond by trying to dig the hole deeper or make the rift wider.
I'm going to close by offering you this.
1. Don't let a prideful desire to prove your mother and your sister wrong allow you to tolerate or make excuses for unacceptable behavior.
2. Look at Peter's motivations. IMO he seems insecure and more driven by proving to others that he can get a beautiful, gorgeous super model wife than by love. I know that's saying a lot for someone who doesn't actually know either of you, but his behavior on the show is telling. Not being there for the Bailey Agency event was not the conduct of a loving, supportive spouse. Publicly embarrassing your sister was not the conduct of a loving, supportive spouse. You are like a trophy prize Peter can carry around to make himself feel like a big man. Mallory is affecting his ability to feel like that big man. I believe he wants to drive a wedge between you and Mallory because he wants to show her that he is in control and she has no influence in your life. Your feelings are irrelevant to him concerning Mallory.
3. It's up to you to build the bridge between Mallory and Peter. Peter has already demonstrated that he's incapable of being the bigger person -- incapable of being the mature adult -- unconcerned by the rift's affect on you. Mallory loves you enough to find a way to get along with your husband if he's willing. I don't think he's willing without some prodding from you.