what connection to use for drain
If trying to join the lines from above the 3" line will cause issues with slope of the 2" line then the thing to do is to do the coupling more from the side of the 3" line. You could cut the 3" line and install a wye fitting with the branch positioned horizontal instead of pointing up. It may be that the branch can even be rotated up a bit from the horizontal side to gain the best fit.

You could then use a size adapter to 2" right off the 3" branch. Then a series of 2" street elbows (22.5 degree elbow) can be used to adapt the direction of the branch to the incoming 2" line.

Using this technique you should be able to get up to about four more inches of slope on the 2" line.