Gafni is "threatening" to have Degel Hatorah faction run independently from Agudat Yisrael faction, if his concerns about fair leadership of the joint party (ie Degel gets more power) are not addressed.

Aguda has been responding that Gafni should stop threatening and if he wants to run alone, he should just go ahead and do it, Aguda will pass the threshold, and only the gedolim, the Moetzes, will decide what they do, not Gafni and his threats.

Now Agudat Yisrael is threatning back. Their threat, though I am not sure why it is a threat, is that if they run independently, they will run jointly with Chabad and with Peleg Yerushalmi instead of with Degel. 

In my opinion this is not much of a threat. It is especially not overly intimidating.

Regarding Chabad, they have never officially supported nay political party in Israeli elections. They at times have unofficially encouraged support for a specific party and at times for a vague political direction, but they never ran their own candidates and never officially supported any party. I find it hard to believe that they will suddenly officially start supporting Agudat Yisrael and maybe even run a joint list with them, though it is possible. Doing so though, should they break with tradition, is hardly a threat. It would bring more votes for the Haredi parties, as many Chabadniks until have supported, or leaned to supporting, candidates like Ben Gvir, and while some surely supported the joint Haredi party, many did not, and an official Chabad position or run would surely get more Chabadniks to vote for the relevant Haredi party instead of for other parties. Degel might lose a few votes form it, probably not too many, but Haredi politics in general would probably gain a lot more votes.

Regarding Peleg, the threat seems to be that Agudat Yisrael would be brining them into the political scene, and Degel and Peleg dont get along. Still not much of a threat, as again it would be increasing the Haredi vote in general, as in previous elections most Peleg people didnt bother to vote because they didnt want to support Degel Hatorah.I would recommend Agudat Yisrael be careful about who they get into bed with and the Peleg extremists are not going to make life easy for them, but it will likely bring in some votes, at least for the one upcoming election, even if they break it off afterwords and dont run again together in the future.