There is the teaching of three natures (trisvabhava) in Yogacara that you should consider here. On the imaginary level it is just like for everyone else. On the dependent level all is interrelated, phenomena are dependent on perception. Being dependent on perception doesn't mean that nothing exists beyond that, it just means that mind defines and interprets what one perceives. And on the ultimate level ideas of perception and perceiver are understood to be interpretations and ideas only. In the end, there is not even a mind one can conceive.
The problem raised, the interaction of mind-streams, is based on the assumption that there are physically-spatially distinct minds. But minds are not bound by space or time, they are immaterial. Another problem here is the idea that Yogacara - or Buddhism generally - should give a comprehensive philosophy. But it doesn't have anything like that. It is the path of liberation, all teachings are meant to assist in getting rid of grasping at thoughts and emotions.
"While teachers of the middle way, mind only, transcendent wisdom, mantra, and other schools may have their own assertions, the fulfillment of those intentions is the same. There is not a single thing that is not contained within mind."
(Gampopa to Düsum Khyenpa, in "The First Karmapa", KTD Pub, p254)
“If you recognize the world of appearance and existence as the mind, realize the mind itself as empty, and have no grasping at the superiority of your realizations — this is the ultimate view."
(Chegom Dzongpa, in "The Book of Kadam", Wisdom Pub, p609)