Mom in new relationship.. Is it bad to disagree

So my mom and dad split up 3 years ago and now my mom has moved on. 
​I'm a little upset about it.. Well angry as well. My dad was in hospital not long ago practically fighting for his life.. My mom had to fly to Australia as my nan was diagnosed with cancer and given 6 months to live. 
​In Australia my mom found a guy.. He's 11 years younger than her and they only met a couple of weeks ago and I've found out that she's got intimate with him already and is claiming to have started developing feelings for him (she says she's falling in love with him) and it's distressed me a lot. 
​I've almost started hating her for it and I feel bad as I know I should be happy for her but I can't help thinking that she's just proved herself as a easy fuck. I don't agree with him or her for it, I beleive that them having sex shouldn't have happened before so soon. Personally the way she's portrayed him has disgusted me, he got her drunk and slept with her. In my mind that shows he has no respect for her as a woman or a person. He claims to have feelings for her but if that was true I'd have thought he would have been willing to get to know her more instead of getting her wasted to get in her pants. 
​It also makes me feel sick that she could be so careless and emotionless. She didn't contact me for a week whilst I was traveling to hospital to try and support my dad even when I begged her to get in touch as I was struggling and I needed to speak with her.  To top it, my nan was in hospital having her radiotherapy treatment and my mom was supposed to be in Australia to look after my nan. She left my nan on her own for 2 days suffering in pain and unable to move and I've just found out she's been rushed to hospital because of it. 
​Am I in the wrong for thinking she's just a easy slut that will jump into bed with anyone that shows her attention?  Should I be happy for her or am I right in being angry and upset with her for this?