can only use right hand to brake reliably, due to disability - safer/possible to modify bike? I'm new here and hoping someone might have thoughts on this - had a look and couldn't find an answer elsewhere! Apologies for the kind of long question, and if it's silly, but any thoughts would be appreciated :)

My situation is this: I ride a simple hybrid bike just to and from work/uni most of the time, though I'd like to get a road bike one day. I  do also like "mountain" biking on flat trails but borrow bikes for this. 

I have very mild cerebral palsy on my left hand side. It affects muscle strength and fine motor skills but only slightly. If I wanted to apply the rear brake, on my left handlebar, it's difficult for me to get up enough force quickly. (steering and controlling bike are totally fine)

I'm great at using the front brakes though, and it's never caused me problems before (I don't go that fast anyway), but I just started wondering, if I want to get a road bike or do more risky mountain biking, perhaps I should consider what's safest and whether modifications would be possible.  

So firstly I'm wondering whether anyone thinks this is worth investigating, or if only front braking should continue to be fine. 

Secondly, if I should try find a way to rear brake, does anyone have any suggestions? Is there any way to control both brakes from my right handlebar (I'm pretty quick and strong on my right, due to always having had to compensate for my left)? Also, when I was a kid, my dad used to find/make me bikes that applied rear brakes when I back-pedalled - is that a thing? (Google directs me to coaster brakes) But I can't remember if I also had a front brake on those bikes.

I'm not good at DIY, due to the lack of fine motor skills from one of my hands, so if I want to go the path of trying a modification I guess I also want to try work out what I'd get charged for it by a store here in Australia.

I may just be overthinking this, but I've always felt kind of nervous on road bikes (only ridden my boyfriend's a couple of times), so if I do want to get into riding one, I want to know I've got the best set up for me. 

Thanks so much!

(also my injury tag  = disability, wanted to create the tag but couldn't due to being new. I felt it might be useful to link it to injury anyway in case someone looks there for answers on how to ride after an injury to a hand)
Generally speaking your off hand should be the front brake, so if you're right handed the front brake should be the left. They can be set up either way, though, especially if you're using cable-driven (non-hydraulic) brakes. Even with hydraulics you should have no problem making the right hand brake the rear. I would highly advise this, as in a panic situation while mountain biking if you grab the front brake hard, you're more than likely going over the bars. 

There are levers that work both brakes. They are out there!



Here is one that pulls 2 cables at the same time, so you could use it to pull both the back and the front brakes.
http://www.jbi.bike/web/checking_product_description.php?part_number=13748

There is also a company called Surestop whose product I believe works off of one lever and won't engage the front brake until the rear is already engaged, thus making it very difficult to catapult yourself over the bars. They are for V brakes only though, I believe.

The backpedalling braking is indeed a coaster brake: you are correct on that note.