Just let me say before hand, I am sorry this is so long... But I felt like I needed to explain the best I could.

I want to be friends with my fiance's ex-wife, but I'm finding it very hard to bring myself to even talking to her.
For one thing, she has it in her head that I spanked SS4. I have never spanked him and I won't. I don't feel that is my place. I have made it clear to his father that the extent of any disciplining I do would be time-out, take away a privilege, stuff like that.
The first words out of her mouth when she spoke to me on the phone were "I haven't met you, but I have heard you spanked my son and he doesn't like you. If you ever raise a hand to my child, I'll have you in court. Just so you know." For clarification, he would not listen when he was told to put his toy up so we could leave and I reminded him that his daddy had told him that if he didn't listen like a big boy, he would get a spanking (we had been having a problem with him not listening). That's all I said to this child, but if you make him do something he doesn't want to do (eat his dinner, take a bath, got to bed, etc.) he "doesn't like you." He's told me on a few occassions that "Mommy says we don't like you." And you can pretty much get any answer you want out of this child, all you have to do is poke and prod for the right answer and ask a question that confuses him. Eventually, he will tell you that the sky is purple and he is supposed to wear socks on his ears. But, I suppose he really doesn't like me. He is always coming home from daycare and telling his daddy that he colored a picture for me. He always wants to play with ME or help me fix breakfast on the weekends. He's like my little shadow when he's with us. So, it's OBVIOUS, he hates me. LOL
Another thing, everytime she calls my fiance, she's always complaining about something. About how my fiance doesn't take care of SS4, he hates coming to our house, how she shouldn't have to do anything while my fiance has to bow to her every need, and he needs to pay her more money. She says she wants "transparency" between the two of them when it comes to SS4. But she just wants to be nosey. She wants my fiance to tell her EVERYTHING about his life and me. I just want to remind her that she had been practically living with her new husband for a few months, then introduced him to my fiance last October as her fiance (their divorce was not final until January of this year), she got pregnant in February (did not mention it to my fiance until around the end of June), and got re-married around the middle of June which she never mentioned until my fiance referred to the guy she married as her fiance (this was around the middle of July).
I don't have any problem talking to her or being friendly to her, but all I hear between she and my fiance is bickering. I don't want to deal with someone like that.
I have had to have chemotherapy and radiation treatment for a brain tumor (thankfully it's benign and shrinking ), so my life has been stressful enough over the past year. Her attitude doesn't help. We don't talk about my condition around SS4, because I think he is too young to understand and based on her reaction to him telling her that I had to go to the hospital, I don't want her knowing my business. (While on one type of chemo, it was hard to keep most food down. I got sick and vomitted one night after eating. He asked what was wrong and I told him I ate too much. I had a doctor appointment the next day, so he told her that I ate too much and had to go to the hospital. She made the comment that she was questioning my mental stability now because of what a 3yr old -at the time- had told her.)
Oh, and I received a message on Facebook from both her and her best friend about a month or so ago, telling me that I have no connection to HER son, that SHE is his mother. All of this because I had listed him on my Facebook page as my son (when I listed it, there was no Step-Son option). Her friend told me I was psycho and had a "Single White Female" issue and that if I wanted to avoid any problems, I would remove it. Both very hateful. I didn't respond to either of them, because that to me is childish and I don't need to give her the satisfaction.
I don't know what to do. I told my fiance that I want to clear the air with her and TRY to be friends (or at least civil). I even thought about buying her a gift for her new baby.
Can anyone give me any advice? I'm at my wits end here.