Is this inappropriate to ask my trainer?

Tell her that your looking for a Young horse to train for yourself and you want it for barrell racing. Ask her if they are for sale and then she will think that you are being serious about it and May consider the idea of selling them to you as she knows your a good rider and you arent gonna abuse them. There's no harm in trying, if she doesnt want you to train them then she will say so. And tell her that if their's days that she doesnt have time to ride them or shes away that you will exercise them for her etc. :)