Today I expect any brand of car less than 2 months old not to have 2 major break downs and sit 15 days at the repair shop. I want to know if this is very unusual for the Disco Sport or it does happen before I make a decision.
Your expectation is unreasonable. If you want human-flight level reliability, look into what it costs to purchase and maintain an airplane. If you want world-class level automotive reliability, look into a brand that has been providing it for years or decades. Rover is, at a minimum, 8-10 years away from competing on quality with those at the top of the heap. And that's only if they want to. They're not a mainstream brand looking to sell cars and trucks to every segment at a volume level as the big boys. They're a niche brand that people have been buying for decades IN SPITE OF what was previously a horrendous reputation for quality. Supermodels don't cook dinner and pick up dirty socks. They don't have to.
In specific to your breakdown, no manufacturer is going to have parts on hand for something like you described at their dealers. And none of the dealers has a tech with any experience repairing them- yet. It may take some time and a few calls back and forth to an engineer to sort through the issue. And maybe some additional parts. And, based on your description, they thought they found it and it ended up being something else, or maybe two concurrent problems.
In addition- there's an old rule that's never been truer than today- never buy the first model-year of any car. Let them work the bugs out. The reality is, the last phase of vehicle development is done with the early buyer. With the level of technology in vehicles today, driven by emissions, fuel economy and safety requirements, plus the ridiculous amount of driver-entertainment features demands, it's absolutely miraculous that any of them are able to see the reliability they are getting.
People buy first model-years for exclusivity. People buy nice brands like Rover for the exclusivity. This is the price.