Hi, Adam. I did deal with a similar situation after we lost my dad. He was killed in an accident in 2000 when he was 57. My mom moved down here near me and met a guy named Butch at church. She dated a couple guys prior to that. They got married about 2004.
I get along fine with him. My sister, Lori, does NOT. My sister works overseas a lot, and I think it felt awfully sudden to her when they got married. She was in Bangladesh when they got married, I think. It had actually been four years, but she was out of the country for most of it. She came back from UAE about 2010 and spent a month or so at my mom's house. They ended up in a horrible fight. I had to go get my sister who was hysterical and crying. I'm not even sure what they were fighting about. She went back to Buffalo, NY, and hasn't spoken to my mom since. I doubt if she ever will.
It is a difficult situation when parents re-marry. I wasn't real happy about it when my mom started dating or got married. We worked through that, and it's ok now for me. He makes my mom happy, so I'm happy for her. I live close and see them all the time, so the adjustment was more gradual for me. I doubt if it ever will be ok for my sister.
If I can help with anything, feel free to ask. I'm glad to see things are improving in your situation. It takes a little at a time. Like Terry said, it's difficult on the other side, too. Just get to know each other and hopefully things will be all right. It's hard on us when parents re-marry, but we have to remember...they lost their spouse. They deserve some happiness, too. It's extremely common for men to re-marry fairly quick after a spouse dies. It isn't anything against your mom. It's what most men do.
I hope things keep getting better for you and your sister. This whole grief thing sucks.