Based on what you've stated, I couldn't justify grinding peanuts in the same room. I started in a spice grinding facility, and we justified multiple production lines in one large room with proper dust collection and sufficient open distance between them. But we performed air sampling to prove this was sufficient, along with showing all product we processed was non-allergen and otherwise low risk.
At a minimum, I'd say you'd need to build some sort of partition between your cheese and peanut lines, processing and packaging would need to be performed wholly in those areas to avoid cross-contamination of in-process materials. Air collection in those areas would need to be considered to prevent leakage out of that partition. You'd also have to consider updating GMP's to ensure employees don't bring contamination from one partition to another, and design your people and product flows accordingly.
It can be done, but it will take a lot of careful (and expensive) evaluation to pass muster through your regulatory and certification bodies.