Is my brothers wife cheating?

So my brother has brought up a concern he has. He says his paranoid side sometimes thinks his wife is cheating. They have a 4 yr old son. She's always away on business trips BTW she works with men. As in every other week. Or sometimes even every week. He says they are having some issues in their marriage. Little ones, not anything big that's not fixable. They do fight, when he tries to make it right And be affectionate she just bickers at him more. He says they haven't had in over a month. She comes home from being away for 2-4 days from business And she just bickers more and they don't make love. He says he loves his wife but is not sure if she is the love of his life. I feel like my brother sincerely does love his wife. He would do anything for her. Sometimes I feel like he plays the mom And dad role since she's never really around. he swears that 99% of him feels like she's not cheating but obviously he has doubts and I tell him go with ur gut instinct! She did cheat on him a loooooong time ago when they were both younger b4 they even got engaged or married. And he did too. The thing that gets to me most is she's always gone and the fact that they don't make love. He says he's lonely. I can tell he just wants her to love him, stop bickering about every little thing. Hold him and feel loved. He says they sleep at different sides of the bed. What Is her deal? Its almost as if she's trying to pick on almost anything just so they can fight. Whats up with all these business trips and her not wanting to be affectionate with him, why does she bicker all the time?