If, for instance, the Senate goes into recess and Trump makes a recess appointment of a new Attorney General, can the Senate meet and reject that appointee upon their return to session or does the appointee automatically get to serve until the end of the year?
To the best of my research, they can "reject" but that doesn't affect the appointment.
Are There any Statutory Constraints on the President’s Recess Appointment Power?
... In addition, although a recess appointee whose nomination to a full term is subsequently rejected by the Senate may continue to serve until the end of the recess appointment, a provision routinely included in an appropriations act may prevent him or her from being paid after the rejection. (See below, “What Happens If the Nomination of a Recess Appointee Is Rejected?”)
What Happens If the Nomination of a Recess Appointee Is Rejected?
Rejection by the Senate does not end the recess appointment. However, a provision of the FY2008 Financial Services and General Government Appropriations Act might prevent an appointee from being paid after his or her rejection. The provision reads, “Hereafter, no part of any appropriation contained in this or any other Act shall be paid to any person for the filling of any position for which he or she has been nominated after the Senate has voted not to approve the nomination of said person.”31 Similar provisions had been included in annual funding measures for most of, if not all of, the prior 50 years. As a practical matter, nominations are rarely rejected by a vote of the full Senate. Rather, some nominations that are not ultimately confirmed are never reported by, or discharged from, committee; some are reported to, but never taken up by, the full Senate; and some are taken up by the Senate but never subject to a vote on confirmation.
Additionally, there's evidence that there's no effective way to end the recess appointment:
This has never been done before (in NLRB case, Senate had to go to SCOTUS to reject Obama's appointment on Constitutional grounds)
Wiki article doesn't mention that as a possibility
Chuck Schumer threatened to stop Trump from doing this, but only mentioned ONE real approach (holding Senate in session, which makes recess appointment impossible as per NRLB SCOTUS decision) - but didn't say anything specific on blocking if appointment does happen.
Heritage founation analysis of NRLB case didn't mention that option
Neither did Harward Law Review analysis on the same topic
Cornell Law says:
... Nonetheless, a constitutional attack upon the status of a federal district judge, given a recess appointment and then withdrawn as a nominee, was rejected by a federal court.
The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session.
There is no provision in that for rejecting nominees.
This is understandable in context. At the time, the Senate would typically meet once a year, after weeks of travel for the farthest members. So a recess appointment would last until the next time that the Senate could meet and approve appointments. There was thus no reason to reject a recess appointment. It would expire at roughly the same time as any rejection would take place.
Generally, when we speak of a rejection of a recess appointment, we mean that the permanent appointment was rejected. As intended, the recess appointment is meant to be a temporary appointment until the Senate is back. So the president makes the recess appointment and a more permanent nomination. The recess appointment allows the immediate work to be done. The real nomination requires the normal consent of the Senate and can be rejected. But rejection does not end the recess appointment, which lasts until "the End of their next Session."
Modernly everyone is only hours away by airplane. The Senate meets multiple times a year, and recesses aren't much longer than a month at a time. It would make sense for a recess appointment only to last for a few months or for the Senate to be able to rescind it. But there is no process to rescind it, so a constitutional amendment would be needed to provide one.
Courts could have ruled that intrasession appointments only last until the next adjournment of the Senate. But the actual practice has been to allow appointments to last to the adjournment sine die after the start of a new session following an adjournment sine die. This has the odd effect of making intrasession appointments last longer than intersession appointments.
Unless and until someone amends the constitution to provide a more rational system, this is how it works.