Steven,

These are great questions. 

Yes, you would want to choose a amine formulation of triclopyr, not an ester to try to avoid penetrating the bark of the tree and causing damage to it. Usually the ones you want are numbered "3" (e.g. Garlon 3 has the triethylamine salt formulation of triclopyr). The amine formulations are water soluble, not oil soluble like the esters. You would not want to add any oil as #1 it won't mix well and #2 oil is what helps provide penetration through bark when your intent is to kill trees/shrubs . 

Times you would want to avoid spraying triclopyr on the bark altogether include: some tree/shrub species naturally have very thin bark, if the bark is green or damaged, if there are suckers present. These can be entry routes for herbicides and may lead to some degree of injury.

If you are not going to be treating poison ivy foliage and are just spraying the woody stems, this proposed method likely won't work very well for the same reasons it is less likely to harm the trees.

Another method to consider for controlling the poison ivy, though more labor intensive, is to use a cut stump method. In this case you cut the poison ivy close to the ground and treat the cut connected to the roots with concentrated triclopyr (within a few minutes). There should be instructions for this on the herbicide label. This method can help avoid movement of your herbicide. There's a great, short video you can watch on this from Penn State Extension: https://extension.psu.edu/cut-stump-herbicide-treatment
*Note you would still not want to use an oil soluble formulation due to proximity with the trees. You can also dab the herbicides on with a foam brush or a dabber (sold on Amazon or other retailers). 

Please let me know if you have more questions.