I've been amused recently by the US Republican party struggling to pass healthcare legislation, and by Mitch McConnell's mixed metaphor of it being a Rubik's Cube that somehow has "dials that need to be turned just right." The Republicans have a majority in the House and Senate, and they also have a Republican president. They thought passing legislation would be a cakewalk. Yet they still struggle mightily, because the various conservative and moderate factions are unable to compromise. Is there a term for a political party that has this problem? I think countries that have more than two major parties are likely to see this issue more. The extreme political polarity in the US today makes this issue more pronounced than before.
You might call the party a splintered party. This phrase has currency, as evidenced here.
The party might be said to be experiencing infighting, defined as follows:
prolonged and often bitter dissension or rivalry among members of a group or organization (Merriam-Webster).
The party might also be said to be in turmoil, defined as follows:
a state or condition of extreme confusion, agitation, or commotion (Merriam-Webster).
Although turmoil is a general term, it has political connotations. See here.