In any case the dual disclosed agent should explain all of your options to you including using in-house or an outside source for your loan.
My broker has an affiliated mortgage brokerage. I offer my clients "outside sources" and "in-house" and let them choose without persuasion.
One thing to remember is that Realtors are like independent contractors. Even though 2 Realtors work for the same company, they have their own client's needs in mind.
As far as the loan goes, I always recommend tyo my clients go to at least 2 loan specialists so they know they are getting the best package available.
In truth, one Real Estate Company can preform all 3 of the roles you have described in your letter. The part that is most important is that you feel you are being fairly represented. You must feel that the agent is there to advocate for you, and that you are getting the best deal possible. If you do not feel this way, have a heart to heart with your agent, and tell them why you feel uncomfortable. Communication is key to a successful outcome.
Selecting an agent who is affiliated with your lending institution is not necessarily a bad thing, so long as they are introducing you to a capable, knowledgeable, and ethical agent. There are some larger, more dominant companies in the Sacramento area that list and sell many properties. You could drive yourself crazy trying to find an agent with a different company affiliation than the listing agent of a house you like. I would find an agent you trust and stick with him/her. Good luck to you.
Understand that the actual contract is with the broker, so the broker may be in what's called a dual agency relationship with you. But the agent realtor who WORKS for that broker can be a different person.
Hopefully I said this clearly, but I think dual agency is fine, as long as there's different representation for the buyer and seller. (Others will disagree).