I doubt you'll be able to straighten it without digging out one side; however, you should be able to bend it easily enough and - given time - you should be able to get the part above your bending point straight.
If you want to bend it, this is what I would do...
- Get some 1/2" dacron rope. Not nylon, not hemp, not the floating garbage, DACRON.
- Dig an angled, 4' deep hole as far away as the tree as possible and set an 8' 4x4 in it at a 45 degree angle leaning away from the tree. Cut a notch/groove around the top of the 4x4 maybe 3" from the end.
- Take a couple of turns of the 1/2" line around the 4x4 in the notch. Make them loose so that when you tie the ends you have loops about 8" in diameter that hang
- Make similar loops around the tree trunk as high up as possible and make more of them...enough so that when they are pushed together they cover 6-8" of the trunk so that the stress that will be applied is spread over a larger area and does no or less injury to the tree..
- Tie one end of a long length of the 1/2" line to one of the loops - either those on the tree or those on the post, doesn't matter.
- Now run your 1/2" line thru the other loops and back. Do it 3-4 times
- You now have a rudimentary block and tackle with tons of mechanical leverage...start hauling on the bitter end. The tree WILL bend. Since there are no sheaves, there will be a lot of friction. That is good as it enables you to pull on something other than the bitter end and have things stay put while you then pull out the bitter end. If you happen to have some blocks, NP in using them, this way saves $$ if you don't have.
- Once you have bent the trunk as much as possible or practicable, tie off the bitter end to the block & tackle line parts.
- Take some smaller line - 1/4" nylon would be good - and use it to whip together the loops left in #3 & #4 above starting at the part closest to your rudimentary block and tackle. As you pull this line taut you are closing the loops and that will bend the trunk a bit more. You may not be able to totally "whip" the loops which is OK, do as much as possible and tie off the end of the whipping line.
- After a month or two, repeat the above and see if you can bend the trunk a bit more; maybe yes, maybe no...the trunk needs to grow a bit to help hold it in the bent shape.
You said there were two trunks - don't try to bend both with one setup, do them individually.
If you can't bend it as above, let me know and I'll tell you how to rig a Spanish burton (purchase on purchase) :)