The DUP are hard Brexiteers. They don’t want the back stop sorted - they just don’t want it all and believe that neither the UK nor the EU would impose a hard border (they are probably wrong on that – the EU will make the Irish introduce border controls to protect their Single Market).
There is no chance that the DUP would support the current Labour leadership in a no confidence vote. Corbyn is a friend of the pIRA and the Republican cause. The support of the DUP might not even be crucial, however, as I think The Independent Group might well vote with the government in a no confidence vote – they have not exactly been treated in an adult fashion by the Labour Party, with threats of them being ‘crushed’ etc. and they are in no position to fight a General Election at the moment. I’m not entirely convinced that Labour should want a GE either – The Independent Group are being very successful at attracting moderate Left Labour voters, with the latest opinion polls showing support for TIG at 18% and that for Labour down to 23%.
If its actors you are after, you should ask raging.