By Paul Carrel

BERLIN (Reuters) - German Chancellor Angela Merkel's conservative 'Union' is anything but unified, with her Bavarian allies preparing to hold their annual party conference without her as the alliance struggles to repair divisions over her open-door migrant policy.

A year ago, the Bavarians' leader, Horst Seehofer, embarrassed Merkel by criticizing her in front of his Christian Social Union (CSU) party faithful for failing to put a cap, or "Obergrenze", on the number of refugees entering Germany.

This year, Seehofer and Merkel have agreed to each stay away from the other's party conference - a split that is holding up a widely expected announcement from her that she will seek a fourth term as chancellor next year.

"We know what an internationally recognized chancellor she is - that is obvious," Bavarian state Finance Minister Markus Soeder told German broadcaster ARD. "Nevertheless, the issues will be discussed first and then the personnel."

The CSU is sister party to Merkel's Christian Democrats (CDU), and together they form 'The Union'. But angst in the fiercely proud and traditional CSU about last year's influx of almost a million migrants has sown discord between the allies.

Merkel has repeatedly rejected a migrants cap on the grounds it would be impossible to enforce.

Soeder, a potential successor to Seehofer, refused to say he would support Merkel as the chancellor candidate backed by the CSU, which is sister party to Merkel's CDU.

The CSU, which holds its conference on Nov. 4-5, faces a regional election in 2018 and is worried about losing votes to the anti-immigration Alternative for Germany (AfD), which has punished the CDU in other state votes this year.

Leading resolutions for debate at the CSU conference are "political Islam is the greatest challenge of our time" and "prevent a slide to the left - so that Germany remains Germany".

The hard-line tone reflects concerns about the party losing its absolute majority in Bavaria. A poll for SAT.1 Bayern on Thursday put support for the party at 44 percent, with other parties that would get into the regional assembly on 49 percent.

CDU and CSU officials say that by not attending each other's conferences, Merkel and Seehofer recognize it is in their mutual interests to avoid clashes while they resolve their differences, and before campaigning together for next year's election.

The CDU holds its party conference in early December.

Keeping some tension over the migrants issue with Merkel, a Protestant pastor's daughter who grew up in communist East Germany, is in the interests of Seehofer as he tries to stem any further erosion of support to the AfD and parties on the left.

Catholic Bavaria was the point of arrival for most of the nearly 1 million migrants who arrived in Germany last year.

In a television program broadcast earlier this year, Seehofer showed off an elaborate train-set at his home which features a figurine of Merkel standing at the main station.

"In relaxed times between me and the chancellor, she is the boss of the complex," he said standing proudly over the train set, before revealing that he moves her figurine to the window sill when they argue. "In difficult times: window sill."

(Additional reporting by Andreas Rinke; Editing by Richard Balmforth)