OP, I was in your position several years ago with a little gelding I’d raised from a newborn foal. He was a nice horse, jumped around small courses, had a flying change, was extremely mannerly and sweet. Just a good boy, but I didn’t enjoy riding him for whatever reason (strange since I broke and trained him). Like your girl, he was kind of sensitive, and I worried about him in a new home, especially since he’d been with me his entire life. I wound up re-homing him into what I figured was an ideal situation. Two years later he was dead. It’s a long story, but my healthy, fat, shiny, happy boy turned into a rack of bones with a scraggly coat, chronic ulcers, and was just miserable despite how much his new owner loved him and tried to help him. He colicked a few times and they had to put him down during the last bout. He’d never colicked in his life when I owned him.
I tell you all of this to say, you cannot know for certain the future of your mare when she leaves your custody. If I had it to do over again, I would’ve leased my gelding out and made sure that if/when he started having trouble or it was obvious the arrangement wasn’t suiting him, I could get him back. He’d still be alive today, I have no doubt of that.
You could lease your mare off-site, maybe even at your client with the indoor’s place if there is room? That way the mare can be in a place that caters to the kind of riding she prefers, someone else gets a nice hunter to ride and show without the financial plunge of buying, your client could get some money for boarding the mare, and you retain ultimate control over what happens to her. And when/if you decide, you can terminate the lease, breed her, and bring her home to let her be a broodie. She might produce your dream eventer in the future.
I think sometimes we should listen to our hearts when those special horses come along and enter our lives. After my experience with my little gelding, I will never let a horse I love leave if I can help it. The three I have now are in their forever home with me, and because two of them are retired and one is not exactly my ideal riding horse, I have chosen to put off buying anything else until either one of my old retirees passes away or I win the lottery. By the time that happens, I may be too old to care about getting a new horse, LOL.
Good luck in whatever you choose to do.