Sump Pump to Rain Barrel Collection & Tree Watering?

The back corner of our house is kinda a forgotten area. It's almost all rocks, on a pretty hefty slope (walkout/basement level back there), and we don't end up over there much. There is a tree or two back there that we put in a year or two ago in the hopes that they will grow tall and block a window or two from direct view of our neighbors. Also, the sump pump more or less dumps out directly onto the rocks there and ends up with a bit of a swampy back corner of the property, before it more or less drains slowly out into the small open space area. The trees are aspens, and seem to be doing ok, but they are not growing as fast as some our neighbors have, more or less for the same reason - I'm assuming it's because the small drip line doesn't end up dropping enough water for it to really thrive, and with the tree being more or less hidden on that side of the house, I never think to get over there and water it by hand.

Originally, we were thinking of hooking the sump output up to an underground pipe that would eventually meet up with a perf. pipe along the fenceline to encourage better drainage. But I was wondering the other day if it would be reasonable to hook up a rain barrel to the downspout and sump pump over there, and hijack the water so it would slow-water the tree. I didn't see a lot of info on this online - anybody do anything similar? I'd probably be looking for a half barrel or wide/something with at least a lower height, so the sump didn't have to try to push the water up an extra foot or two, with a slow soaker or similar hose around the tree for the dry weeks, and the overflow then flowing away or maybe eventually into the underground pipe for when it really rains hard.

Any thoughts? Anybody try something similar or know of any kits that are set up for this?

Barrel and two bulkhead fittings should do it. The pump shouldn't have much issues adding a couple of feet of height. The real challenge is winterization

Well that's a good point, hadn't even started to think about winterizing rain barrels, let alone something hooked to the sump. Might not be worth it, maybe I just run a few more drip lines or something.

Winterization of the rain barrel is easy. Just turn it sideways after getting it mostly empty. It's the sump pump that would take some thought. Maybe just french drain the swampy area over to the trees for a passive system?