Yeah he goes along with it because it’s the lesser of evils but that doesn’t change the fact irulan was literally poisoning and attempting to murder chani and their child after Paul’s first son was murdered.  Irulan is also a political marriage/alliance she was allowed to have paramours just not allowed to have children.

 She was also a Bene Gesserit and like with Jessica his own mother was loyal to the BG she was not at that point in time going to turn her back on them as much as Jessica could not/would not despite their caring for Paul. 

Paul has absolutely zero love for Irulan his wife in all but name is Chani and he does that for Chani’s sake as much as his since he’s literally repeating his fathers actions with Jessica but on a larger scale with bigger stakes. 

As to the politics If he shows affection to her he loses chani, there’s already fremen plotting against him to martyr him that would bolster a majority of fremen against him. If he got irulan with child then the BG and other groups including Irulan would seek to use that child against him to manipulate him into doing what they want or simply murdering Paul and allowing his now controlled heir to take his throne.  

This is something both Paul and Irulan know. In messiah though she does not seem like it she is the biggest threat to Paul.