How you word it is far less important than getting it in front of the right people. The best worded resume in the world will mean nothing if it is never seen by the people making the decisions. Your goal should be to:
- Get the blessing of your manager
- Find a well-connected HR contact in the new company
- Create a speaking relationship with people in the other organization
Get the Blessing of your Manager
Your bosses may not be responsible for deciding if you can transfer, but they can probably raise a stink and prevent it from being an easy task. I'd recommend sitting down and asking for their blessing. I would focus on the following points:
- I really like working with you
- I really like the company...
- ...but my commute is killing me
- How can we find a solution?
Perhaps something like this:
Hey boss, I really appreciate your support over the past X years. You've really helped me feel comfortable in this organization, and helped me get better at my job. I feel like this company is a very good fit for me, and I hope that you can help me out a little more.
As you know, I recently bought a house in [Location] which is X minutes away from here. As much as I love this job, the commute is really becoming a struggle. I am looking for ways to stay with the company and reduce that commute.
We have a sister company in [Location] which is much closer to where I live, but unfortunately there aren't any openings on the intra-company transfer site right now. I was wondering if you would help me find a way to move to that company in the next few months if possible, and if you have any other suggestions on how to make this work.
I know that it will be a bit of added work for you while you find a replacement and train them up, so I am more than happy to do what I can to reduce the burden on you.
The goal is to say to your manager, "I really want to do what I can for you and the company, and I want to do what I can to make this easy for you". Your manager will have a hard time refusing the request even if they don't want you to leave, and if they are happy to help you out they may even negotiate something like working from home a day a week until something opens up. At any rate, you want to make sure you are honest with your boss and get their blessing, as chances are the other company will be calling them up to speak about you.
Making sure they know what's up is a key to success.
The Right People
Getting hired within your company requires an inside-person. Each company has those super-talented people who just get things done because they know the right people. You want to find that person (or someone close to them) to maximize your chances.
If your company rarely speaks with people from that company, then a open application is likely to be thrown in a stack and forgotten (who is supposed to manage an intra-company transfer application for a non-specific role?). A speaking relationship with someone in that company will make you a real person and give you an advocate in that organization.
If your HR department has a contact person in that company to send applications to, ask who it is and give them a call to explain your situation. If the HR people in your company are reluctant to do that for whatever reason, schedule an afternoon off and go visit the company you want to apply to, calling ahead (at least a week) to explain that you work at company A, recently moved closer to company B, and would like to see the office and have a chat with HR to see if it would be a good fit even if there isn't a position open at the moment.
At the end of the day, whatever method you use, your goal is to find a contact within HR who you get along with decently and would feel comfortable with chatting every now and again (and who hopefully feels the same about you).
Business is about people.
There is no need to be fake or a salesman, but leverage your contact. You can honestly ask your contact, "I would love to learn a bit more about what it's like working for Company B, would you be willing to discuss it over drinks sometime?"
Disclaimer: Change drinks for coffee or whatever is appropriate. Be careful if the person is the opposite gender. All standard common-sense rules apply for human interaction and I'm not going to list them all out.
If you actually get along decently with them, meeting up with their friends inside the company every now and again will help build a network. If people know your face, your chances of being put in touch with the right person inside the company dramatically increase. Rather than just being suggested for positions specifically opened up for intra-company transfers, you have a chance at having people work to find you a place (or even create one where one doesn't exist).
Speaking with your boss may allow you to lessen the burden and make it easier to tolerate the commute for months. If I were you I'd set a personal deadline for how long you're willing to wait:
"If no opportunities open up in that company by October, I will start looking for other jobs."
(Obviously this shouldn't be shared with the employer)
In the meantime, I would patiently wait it out, and focus on being the best employee possible. That will both increase your chances of getting a sparkling recommendation for your boss if a position does open up, and give you an internal backstop to make it easier to tolerate the commute (we all do better when we know it will end at some point).