It all depends on the soil types between the two. Sounds like an unusual "correction" situation. I'd shoot for a discharge of the drain system well away on the surface. No "infiltration" system or "storage'. In these situations I "waterproofed" the ground surfaces area within 15 feet of the house, all directions. I've written about this several times a various posts on this web site.
Not sure you find that posting, but using the words "bentonite" and maybe "drainage' and you will find it. If needed, I can repeat it here.