Eric Ries intimated in "Lean Startup" that nobody would steal our ideas, but I have concerns with an external agency or developers having possession of source code that would be the core of our business. Is this an unfounded fear? When funding permits, I would like to explore having an in-house development team, but quality agencies and developers seem to be available to hire in abundance. If my startup is bringing in revenue and profiting, is it unusual to continue a working relationship by outsourcing development to a third party? I'm thinking in the most economical sense, that this is sensible, however there are certainly other concerns to consider.
Some great responses here that I won't try and reiterate, but the one model that hasn't yet been mentioned (at least from my reading) is a hybrid model built on the ages-old business advice around keeping your core capabilities internal and outsourcing the rest.
If I were in your shoes, I would be hiring or partnering with a technical architect who can craft the design of the technical solution with aligned interests in mind (being a member of your team). Then, you outsource the engineering work based on whatever model works for you (personally, I would have the technical architect hand-pick resources), and use them surgically to deliver parts. This way you have the best talent to deliver the work they are best at, and your distributed model reduces the risk of theft of IP (although IP ownership is usually covered in a good contract).
You also need to decide if what you are building is actually an MVP, or if you intend on the resulting solution to form the foundation of your eventual product. If it's disposable, you don't need to spend a lot of resources getting to something that can communicate a concept. In fact, what you probably need for that is just a good UI designer who can build wireframes. Don't get too hung up on a fully functioning MVP. My best and most useful conversations have come from customers who see nothing working yet but can visualise the concept enough for me to get information on whether to stay the course, or pivot.