The answer is simply that the first predictor (as found from left to right in the original data frame) is selected. See this thread for the proof. So, to sort everything out:
Will there be any difference between choosing any of the two
attributes to be a tree node?
No, selecting one or the other makes absolutely no difference.
So for text classification, it will check in the alphabetical order.
This is only true to the extent that (the columns of) the data frame of predictors are ordered alphabetically.
You could look ahead at the information gain of the remaining
attributes after a split and select based on that.
This is not a bad idea and is doable by hand for a small tree, but that's definitely not what's implemented in CART. First, it would be very expensive: imagine for a big tree, all the combinations that one would have to try. More importantly, this goes against the idea of recursive partitioning where at each step, the best predictor can be determined simply as the one that yields the best partition of the current node. This process is conditional on the previous splits (the current node was created by the previous splits); it's not the other way around. CART is inherently greedy and it was shown that looking ahead did not give significantly better results, see this PhD thesis section 2.5.4.
Can you try both trees, and see which creates a better separation at
your terminal nodes and/or builds a tree that fits more closely with
the theoretical understanding you have of your data?
Again, with a large number of predictors, the numbers of trees to try would be immense. Further, machine learning is often used when the understanding of the relationship between input and output variables is very limited (otherwise, an explicit model could be specified, see this paper), so making a decision based on theoretical understanding is most of the time not possible. Finally, CART trees are usually the base models of ensembles such as RForest and Boosting, where large numbers of trees are automatically grown, so it is completely impossible to inject any kind of human-understanding into the tree-building process in these cases.