Mom talking to other guy - what to do?

Background: my mom is 3x divorced (twice to the same guy), met this guy (C) in August 2016 and married for the 4th time to C in December 2017. Me, my fiancé, and our baby live with C and my mom (plus my younger brother). We’ve been living here since baby was born, so about 9 months.

I don’t know how long it’s been going on exactly, but my mom has been texting her old fwb for at least a few months. He was her fwb before she met C but she broke it off with him because he didn’t want a committed relationship. I don’t think she’s physically cheated on him but she had plans to a few weeks until but C changed his plans so she couldn’t.

Then she tried telling me they’re just friends who talk now, but if they were just friends she wouldn’t keep his chat on silent so his messages don’t pop up, or hide it from C. Last night she got freaked out because C tried grabbing her phone and she had a message from the “friend” on it.

My mom is my best friend and that’s why she told me, and she asked me not to tell him. And the other thing is, I really, really dislike C. He has this overall angry and negative attitude. Constantly complaining about everything, from the baby’s bedtime to my cats to us living here in general. My mom doesn’t care at all that we live here, and shes the one who makes their money. My mom makes close to 60,000/year whereas C doesn’t make more than my fiancé and I do. He was living with his ex-gf’s parents before he met my mom. He even had the opportunity to apply for a job making 70,000/year, and he refused to even apply. That’s almost 3x what he makes now. Not my business but my mom raised 3 kids on her own and deserves a financially stable household. She was pretty upset when he wouldn’t do it. He also has these dumb beliefs like “all people who smoke weed are deadbeats” and “if you don’t make enough money get a better job” (like I hadn’t thought of that 🙄) and even told my mom I shouldn’t be in college because I should be working (hello, I AM WORKING.)

In general, he’s a dick. But at the same time, I have strong morals against cheating. Also, it would end their relationship, which seriously needs to end. My mom isn’t happy at all (hence the cheating) but won’t break up with him either because she doesn’t want another divorce. If only shed listened when we told her not to get married so soon...

So I guess I don’t know what to do. I don’t want to make my mom mad but dude barely contributes to the household, is constantly bitching, makes us all uncomfortable, and it just isn’t a happy relationship. My fiancé and I will be moving out in a few months so it won’t be our problem after that but still. I can’t even hang out with my mom anymore with him around because it’s so uncomfortable.