A few thoughts...
If you have an extra wide crank then you also have room for a centrifugal clutch. I had a couple of these. I ran one for a year and loved it until the clutch stopped engaging with the motor and by then a part was worn inside the clutch assembly and I did a lot of struggling trying to get that fixed. I think eventually I would have. I also had bought a second one, having liked the first so much and bought it from the same seller, BGF. This one was a lemon from the start. with a number of problems but mostly that the clutch worked for a minute and quit engaging. I learned along the way some tips from Rockenstein which would have kept the first one from going bad in the first place. Others here, just a few, have automatic china girls and have had good luck with them. When they work, I like them. If they don't engage you can't go anywhere. I lost both engines in a fire, so never did get things resolved. If I were to do this again I would either research vendors (few offer an automatic) to see if one has a reputation for making things right and go with that. Rick is an OK guy at BGF, but his prices are low and so is the level of customer service. He does a high volume of sales and communication is sometimes poor. In his own way he did try to help make things more right, but replacing that second engine was never an option in his mind. A good vendor would have, especially from a repeat customer. I think instead, if I were you I would consider using an engine I already have, adding a pull start kit and an automatic clutch kit. That way you will always be able to return the motor to manual and will already have the parts for that. By assembling the automatic kit you'll have insight into how things work and can make sure things are right with it before you ever use it. If a vendor sells you a bad automatic kit, and is a good vendor, you can get resolution. Again, when mine worked, it was a charm. In your situation, with a bigger sprocket on the rear wheel it would be a winner.
20 mph is a good top speed I think for the bike with sidecar. You could always add gearing to it later and a number of smart folks on this forum are at this moment working on viable options and of course the SBP shift kit will always remain an attractive option which is proven to be a good setup.
If that is still a Worksman wheel on the back I would keep that coaster brake as it is and as Curtis suggested, just clean it up and grease the bearings. Take a look at the front fork where the fenders attach and see if a front caliper brake could go there. For awhile I had one on my Worksman from a BMX bike and it worked well enough and much better than no brake at all up there. A front drum brake is great, but means changing out that front wheel and if it is Worksman right now I'd consider leaving it if the caliper brake is an option. You are not going at high speed, so braking power in your case has more to do with the not so great extra weight of the sidecar and possibly much greater weight if a passenger is riding along. Where I would consider really beefing up the brake (this is if the wheels on the bike part are good wheels right now)... would be on the sidecar where making modifications would be simpler an that wheel looks more iffy. That looks like a full sized wheel, either 24" or 26" so if you could set that up with a drum brake or disc brake(those I know less about and have never had one) you could use a double pull brake lever and operate both sidecar and front wheel brake with one lever. I think you could do pretty well with that setup. I know others will say to have disc brakes on all the wheels, but I'm assuming you are on a budget, so I'm advising as I would do it myself, on a shoestring budget. Sometimes you can find used Worksman wheels on ebay and could always upgrade your front wheel later on.
So you could do this build in progressive stages, upgrading as you can afford it. From the start I would get an extra wide one piece pedal crank. Worksman sells different sized sprockets for the pedal side of the rear wheel, so you could make it easier to pedal when you wanted. Even with an automatic you may want to help out a bit by pedaling from a dead stop or going up a steep incline. A different sprocket on the rear wheel can make that an easier thing. A pull start kit. An offset intake manifold from Spooky Tooth so you have a bit more room for the engine (about ten bucks with shipping). And a bigger driven sprocket engine side of the rear wheel. Later add the automatic, the brake improvements,shift kit or whatever as you can afford it. Oh, and some kind of brake up front right away, even if just caliper. I think you can have a good rig that is a pleasure to look at and ride for not too much money. If you want to have an in frame motor, you pretty much have to go with the china girl as it is the only thing I know of which will fit without frame modifications. If you're O.K. with a rear rack mount engine then everything changes and you'll need to ask somebody else. I only know about in frame and not all that much about those.
Good luck.
SB
