I have to admit I too find it rather interesting.... even strange....that your vet would recommend the AlphaTrak meter if they are using a One Touch human meter. I think that is a question only your vet can answer as it would seem they are familiar with the differences in the readings and comfortable working with a human meter.
The difference in the readings between pet and human meters is not a straight linear or % calculation. I have found the difference seems to be greater the higher the reading but there is no simple math calculation to translate one to the other. Even two human meters will not read exactly the same so buying another meter is only going to add to the confusion. It is best to pick a meter and stick with it. The consistency of your readings is the important factor here rather than which type of meter you choose to use. Just make sure your vet knows which meter you are using.
You didn't say which test solution you were using but since you got a AlphaTrak kit and human meters do not usually come with test solution, I assume you used the AT control solution. I presume the difference between control solutions is, at least in part, the sugar concentration. There may be other chemicals in the different solutions that could also skew results. The larger control range on the AlphaTrak meter is because the meter has to be coded to read different types of animal blood all of which have their own "normal" ranges, so the test range has to include a larger number of possible ranges. Technically it might be possible to say if the meter is set on code "X" the control range is between Y and Z but given the number of possible codes in the meter, the list would be too long and much more confusing so they have just combined them into one large range.
Your human meter will work just fine and will definitely be the more economical choice. The strips for the AT meter are expensive. Not sure what they cost in the US but here in Canada, they are more than double the cost of those for average priced meter strips. The AT strips are not readily available at your local pharmacy and will have to be purchased through the vet's office or online so you will need to ensure you reorder in plenty of time to avoid not having strips when and if you really need them.
All the reference numbers in the documentation on this board are based on human meter readings unless specifically stated otherwise so if your vet does have any reservations about you using a human meter, you could print off some of the documentation so they can familiarize themselves with the references used here.