What is the purpose of your question? Do you want validation for your reasons for not getting to know another mom? Whatever your reasons you do have the right to choose who you allow to become friends and who you don't. I suggest that you'll be happier if you judge less and just say to yourself that you don't want to get to know her better. There are so many moms in your world that you don't have time to get to know them all anyway.
About the mom with the bully for a kid. What is our reason for going to church? Seems like the mom with the bully needs the love and support of fellow church goers just as much if not more than the mom with well behaved kids. Remember that kids are born with their own temperaments and in some cases disabilities. Stop blaming the parents, exclusively. IF the parent needs help, judgment is counter productive.
What are your reasons for going to church? If it's purely for social interaction then the bully and his mother won't fit. You can still just ignore them. You don't need an excuse to not befriend them.
Yes, I also get drained listening to vents, even when they're legitimate. It's my job to limit my exposure so that I can stay healthy in the way I think and live. You can choose to not listen.
It's good to not trust a back stabber. But you don't have to be unhappy with them. Again, avoid them.
And the secret to not letting other women upset you when they're flirtatious with your man, is to work on your communication with your man so that you can trust him.
How you react to anyone is your choice. Choose happiness by accepting people as they are without the need to judge before you choose friends. You do not have to be everyone's friend. Choose wisely in a calm way without feeling the need to justify your choices.