Your carb should not act differently in forward or reverse unless you have a massive air leak and bad motor or stabilizer bar mounts. You may want to check your engine ground(s) also which is easily done by using a jumper cable between the block and front sub frame. By pulling the choke out a small amount (presuming) you are just giving the car a fast idle which may be overcoming the possible ground issue with the higher revs. Just a thought.

Years ago, I had an Austin America and it was running rough, and it was easy to shift the car to neutral at the stop lights and shift back into gear when the light changed. It was shortly after that I was pulling the automatic out to fix. It was a broken circlip that holds the forward clutch pieces all together. To this day, I believe that is what kills most automatics! So, please tune-up your car, plugs, points, and distributor cap.

In reverse it idles perfectly, but in drive it stumbles, and yet when you pull the choke out it recovers.

please define pulling the choke out, what that means to you. If the engine is warm and you pull the choke out it will stumble, unless you only pull it out a bit, and then you will have a faster idle.

Is this different in 1 than in D?

when was the oil last changed? I ask this because oil is important with the mini automatic. The engine should be loaded similarly in R as in D or 1-2-3 for that matter. 

The carburettor would be my last suspiscion for this issue, however, feel free to study how an SU carb works and is adjusted, there is a lot you can learn.

I have a 1977 Mk4 Automatic and after bringing it out again for the summer, I have realized that when I put it into Drive, the car runs super rough and dies unless I pull the choke, where it runs fine. In neutral and reverse it idles perfectly. Anyone know what this could be? I was thinking its time for a new carb but I am clueless when it comes to carburetors (im 20 and I was never taught carbs in my auto shop class), and im still learning the in's and outs on the Classic Mini's after owning 3 New MINI's.

Thanks!