How do we pray for others, keeping their agency in mind?

This is a topic I have been thinking a lot about lately.  I live quite a distance from my family, so there is very little I can physically do for them.  So, I pray for them.  In general, I pray for their safety, and happiness, but that is very broad and sometimes we need more specific help.
When I got home from my mission, I met a friend, we'll call her Alice, who was not a member of The Church of Jesus Christ of Latter-day Saints, and the circumstances in her life were such that I thought sharing the Gospel with her would be helpful in her life.  The problem was that she already had a church that she went to and she had no interest in what I had to share with her.  I was never pushy about it.  When the topic of beliefs came up, I was very honest with her, but I never tried to "sell" her anything.  However, I always felt uneasy about the situation.  I could see big gaps of sadness and misunderstanding that could be filled with the glory of the Gospel, but I could also see a lot of fear in searching any other religion than the one she was raised in for answers.

I decided to talk the situation over with another good friend, we'll call her Karen, who is a member of my church and who could understand where I was coming from.  I hadn't counted on Karen understanding where Alice was coming from just as well as she understood me.  She was able to lend me insight to the fact that what I wanted for Alice was not what she wanted for herself.  With some explanation of difference in doctrine, she helped me to see that what I thought was a common point between Alice and myself, was actually worlds apart.  What I thought she wanted, she actually didn't want.  I thought she wanted Disney Land, but she knew the county fair, and she was happy with the county fair and didn't want Disney Land at all.  I thought, well, of course she would want Disney Land, because it's bigger and better than the county fair.  True, it costs more, but it is worth the cost, so of course.  I learned from this experience that sometimes for some people the cost is too high and not worth it when you already have something that works perfectly well right in front of you. 

Now, for a different story, I had another friend who's family were all church goers all her life.  She had a big brother that she looked up to whom everyone thought could do no wrong.  He went away to college, and things went down hill for him.  He made some choices that took him away from being an active member of the church, and he remained inactive for many years.  This friend of mine prayed for her brother all the time, and later she confided in me that every month, when she would fast, she would fast for him that he would come back to the Gospel.  That seemed a fairly reasonable and noble thing to do, however, I felt a little uneasy about the situation.  There was something there that I didn't understand that The Lord taught me…well, just recently. 

Here is the lesson: agency.  In the cases of both stories, how do you pray for someone, keeping their agency in mind?  Heavenly Father cannot take away our agency, and cannot act contrary to our agency.  He cannot bless us with a blessing we don't want.  That is why prayer is so important. It is important in our prayers to ask Him for blessings, so that He can actually give them to us.  There are so many blessings He has waiting for us.  We need to ask for these blessings and qualify for them, but He cannot give them to us, even if we qualify for them, if we don't ask for them.  If we do qualify for them and don't ask for them, it is like saving money for years with the intent to buy a car, and then never talking to the dealer.  Sometimes, someone can asks for blessings on our behalf, but we have to want them and qualify for them.  

As I thought about my friend praying and fasting for her older brother, I thought, what if he doesn't want what you're praying for?  What if he is quite happy where he is, and isn't interested in returning to church, ever?  That would be a sad thought indeed, but what if it is true nonetheless? 

Please understand, I am not saying we shouldn't pray for others, and I'm not saying we should not pray on behalf of someone else just in case they don't want what we're praying for.  What I am saying, is maybe we can pray smarter.  What if, instead of just asking for her brother to come back to the church, my friend also prayed that the righteous desires of her brother's heart would be met?  Her added faith to a cause that he desires, that is righteous, could work miracles.  If he's not going to church himself, it might not be much of a stretch to think that he's not praying as regularly.  Maybe he is, and if so, great, she can still add her faith to his on his behalf.   If he is not praying, however, and if he has righteous desires, her asking for them on his behalf, is something that could be helpful.
What if she were to pray that someone would come into her brother's life that would be a good influence on him?  What if I were to pray that Alice would be able to strengthen her relationship with her Savior?  It's something I could honestly say she wanted, and it is something that would enrich her life and help her immensely.  What if we took some time to really think about what that person wants, and what we want for them (happiness), and figure out how we can help them reach their happiness (in righteousness), not ours.  

I think a lot of times agency is something we associate with choice, and choice alone.  I have come to understand that along with choice, agency has to do with desire.  We are not going to make choices contrary to our desire.  We may have a desire to lose weight, but if our desire to eat fast food is stronger than our desire to lose weight, we will make decisions accordingly.  The really cool thing, is that Heavenly Father can do a lot with our desires.  Even if our desire starts out as just a small desire.  Even if we don't quite have a desire for a certain thing yet, but we have a desire to have that desire. He can work with that.  We have to ask for that help though.  Many times, I have prayed and asked Heavenly Father to help my desire in doing x, or to quit doing y, to increase, and He has done it.  Many times, I have seen something I needed to change in myself, but I liked doing it too much, and I had to ask Him to help me develop the desire to want to change.

So, here's the point, how do we pray for someone, keeping their agency in mind? We keep their desires in mind, and if we are unsure of their desires, we pray for their righteous desires to be met.  We pray for Heavenly Father to bless them with blessings He sees fit for them to have at this time.  After all, He knows them better than we do, and He knows their situation, and their needs.  We pray smart, and we pray for them and not for what we want for them.

Questions? Comments? Profound statements? Let me know below.