You better to change your sources, clearly you don't have any info about the agenda of diferrent groups and parties in Iraq. some seek to increase the U.S role in Iraq and reduce Iran's role, and some are against it.
the biggest opposition to American's cooperation in fight against ISIS is the Iran's backed popular forces, there is plenty of their statements about this.
actually it's been U.S who always wanted to have a role in the fight against ISIS (supposedly to reduce Iran's influence and popularity in Iraq) and of course to handle the terrorists the way they like (not annihilating for sure), yet Iraq's popular forces always rejected it.
Iraq popular forces were defeating the ISIS till they reached tikrit, U.S was demanding to cooperate in this operation, yet popular forces threatened if Americans enter this operation, they wont fight.
meanwhile Ebadi finally bowed to Americans pressure and made a secret deal with Americans to let them in.
right before the start of tikrit operation, American aircrafts bombarded this town, so popular forces refused to start the operation, this forced Ebadi to order Iraq army and police forces to start the operation instead, four days passed without any considerable achievement, after this time popular forces who saw their brothers are dying decided to enter the war and two days later tikrit was out of ISIS control.
Ebadi's betrayal to popular forces and his demand to be followed by all armed forces (including the popular forces) created a rage among popular forces and some of their leaders threatened to overthrow the government. for example, Qais al-Khazali the leader of Asa'ib Ahl al-Haq group (the largest armed group) threatened to create an uprising against the Ebadi government to return the matters to the right path, or Iraq's Hezbollah issue a statement and threatened to peel the head skin of anybody who would try against the legitimacy of the popular forces, they were referring to Ebadi.
What you wrote was written in the POV of Iran's interests.
PMU declared Tikrit operation whilst IA wanted to go for another town. There was a power struggle between the IA/Gov and PMU. Power has been shifting in the favor of gov/IA as PMU has been following their commands since Tikrit OP, before that they didn't follow gov chain of command. The IA takeover of Tikrit OP and USAF support for the storming of the center of Tikrit was a good thing, PMU should not be disobeying Baghdad as they did before, they should answer to the state institutions.
Kataib Hezbollah as an organization should not even exist, their troops should be several brigades in the PMU which itself should be a military force solely, they instead operated on the political level which is dangerous to Iraq. US involvement in Iraq of the current level is needed for the reason that neighbors all try to raise forces in Iraq that answer to them.
Abadi's method of working with Americans, Russia and Iran is the most beneficial to Iraq.