It uses Lightning rune instead of COLD, because Cold pierces and kills things WAY TOO FAST lol. To refill hatred with Karlei's Point you need to double hit same mob with Impale. If mob is dead on first hit, you obviously can't hit him second time..
For lowest rifts this might be a problem with very high dps, so i usually use Blood Vengenace passive to completely solve the issue (just like for my no-generator Multishot build), or Seethe instead of Dark Heart.
Even easier option here is to just raise the level of the rift (right now i mostly farm GR70).
1) Fleet Footed (i usually drop Blood Vengeance for this in higher tiers)
2) Steady Aim/Single Out (just for extra dps)
1) Alter the rift level to higher tier if things die WAAAY too fast and you are running out of hatred even with Blood Vengenace.
2) Stack attack speed instead of Area Damage if possible (the best way is to simply have to sets of gear).
3) You need 36% CDR to have permanent uptime of Vengeance. This can be done with one 8% roll on shoulders or anywhere else + diamond in helm and Dawn in Cube. However, if you don't have 8% cdr it's no big deal. The downtime of Vengeance will be just 1 second.
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