"If I ask for time with him without the phone, he gets mad."
Damn! That's not very nice of him.
"When I asked her why she left marks and didn't make him use a condom, she just said he can't keep his mouth shut. She asked him why he didn't just lie."
See that's what scares me. If he tells you he practiced safer sex, how will you know he's telling the truth?
Sounds like A is a bad influence, but it also sounds like your husband is quite complicit with her. I have to say he's acting quite badly. Has he always been like this?
Your choices will be crappo no matter if you decide to stay or leave. If you stay, your kids will start to notice that it's "okay" for Dad to make Mom upset. Setting a good example is one of the best things you can do for your kids. They need to know that it's important to respect one's own boundaries, and to treat one's spouse with respect. You staying around and tolerating your husband's current behavior sends a dangerous message to the kids that could affect them badly later on.
But obviously leaving and possibly fighting over custody and/or visitation is bad for the kids in another way. So this is a damned-if-I-do, damned-if-I-don't type of a situation.
Be really careful with your health here. Your husband ought to get himself tested for a battery of STI's before you even consider resuming intimacy with him. And even then there's the problem of his believability to consider ...
I agree that you deserve better treatment.