Does Emily hate James since she… you know
James's affair with Gordon and separation from Henry happened before Emily arrived on Sodor, and by the time she did, Henry had moved on, and the two were on civil and almost friendly terms.
Emily disapproves of what James did, definitely, and made that disapproval very clear when she learned. But, she did that more to clear the air than out of any real dislike, rather than let it fester.
If James hadn't cheated with Gordon, Henry would likely have never ended the marriage, meaning he wouldn't have been available to date Emily.
James, while neglecting to mention how she knew so much about him, helped Emily with advice about what made Henry happy in the early days of their relationship.
It's also worth considering that James and Henry have a son together and share custody without any legal involvement. Holding on to any hate towards James could risk that coming to an end. Emily loves Henry and her stepson, so having a good relationship with James is especially important.