The normal process for drilling a counter sink is to drill the hole first, then put the (tapered) countersink bit in. However, for a counter bore you want to do the opposite.
To make your counterbore, you'll want to drill the larger counterbore first using something like a Forstner or spade bit, then use the divot left by the bit's pilot spur to center your smaller bit's pilot spur to make the rest of the hole. To get them perfectly aligned, you'd usually do this on a drill press ("pillar drill" or "post drill" outside the US) where you can take your time to get everything nicely lined up then clamp down your work piece.
Since you're doing this on a tree, moving it to the drill press will be a bit difficult.
- You could drill a pilot hole for both bores with a long but small diameter bit, maybe 1/8" diameter. Something big enough to not break at that length and deep enough to get the main bore started in a straight line, yet small enough to accurately capture the pilot spur on the bits you're using. Use this to center both the counterbore and, afterwards, the main bore.
- If you're creative with some ratchet straps, you could, potentially, strap a drill guide (something of a "poor man's drill press") to the tree.
- This should keep the drill centered on the same spot without the pilot hole and keep the drilling motion all in the same plane, allowing you to use the "drill press method" described above of drilling the counterbore first.
- You would probably need to strap down the guide very securely and test it (give it a few tugs, make sure it isn't going anywhere) before you start drilling.
- Despite your confirmation that it won't move, still be very gentle and accurate with the drill to not dislodge it when you're drilling.
- With the vagaries of naturally occurring bark on a naturally growing tree, it
might will require some shims to get the hole to line up in exactly the direction you need it to go into the tree. i.e. just setting it against the bark is no guarantee your hole will line up with whatever is being attached to it. This will take a lot of fiddling to make it right, but should give you an accurately lined up counterbore.
It sounds like the main bore is 1" diameter and the counterbore is 3" diameter. I'm not sure what you're putting into the counterbore, but whichever method you choose, you might consider moving the counterbore bit size up some to accommodate the possibility that they won't be precisely concentric. By making it bigger, whatever sits in the counterbore may be off center in the counterbore, but will have room to be precisely centered over the main bore. I'd imagine that something will cover this, hiding your fudge space so nobody but you will know. If not, well, your secret is out, but at least the tree house will be safely secured to the tree, so who cares.