I bought a 3 pt hoe, hooked it up according to the sparse instructions and used it for 1/2 hour.
Perhaps I didn't give it a chance, but just didn't like the idea of the stress points and what would happen if I worked it too hard. I felt the movement side to side without comfort. My mind and reason told me if I mounted it solidly to the the front loader mounts and the rear axle mount it would be more like a true backhoe, and so it was.
I made a subframe and enjoyed the peace of mind as I pried at roots and rocks without concern. The tractor bounced around as I sawed at stubborn roots. I filled the loader bucket with large rocks to add weight to help stabilize the tractor as I tried to free stumps from the ground, and felt no unease.
I know many here own 3pt backhoes and use them with no concern, perhaps rightly so.
All I can speak of is my experience. I owned a 3pt hoe but felt what I wanted was a solid mounted tool to work rocky ground, so I welded up something that did not used the top link or the bottom links, but secured the hoe while increasing the framing of the entire tractor, thankfully I succeded.
If I was to dig in friendly dirt, (not connecticut) a 3pt hoe might be fine.
disclaimer: I didn't own a tractor/3pt hoe combo made to work together, maybe there would be a difference. Regardless of all this, I wish you well and hope your tractor-hoe combo does everything you need it to.
Good luck................