My latest horse - about 15 months now had never been turned out with other horses - in fact I would think she had never been turned out in actual pasture either for a long time or never at all
She got terribly clingy to her field buddy and was throwing fits when that horse was taken out to work without her but we just ignored it and over quite a short time its all gone away. She never had any issues about going out to work on her own if her friend was in the stable but wasn't happy if it was in the field and constantly leaned to her but again that has all gone away so I think a lot of it was down to insecurity and a lot down to novelty.
As she's reactive I would be careful of anything that she feels is confrontational - and that can be body language as much as holding a whip. I did use the idea of desentizing to a whip as she did see it as a tool of punishment (not what I want) and we are now over that hurdle. I find that when I loose work or lunge a horse that's a bit anzious I can drop the whip when I need too but if they see me as a threat nothing I can do about that
I prefer to start out an 'iffy' horse on the lunge as having that contact between me and them reinforces my control and keeps everything very disciplined, once that's established a move on to loose work
Our methods are slightly different anyway in the UK