Is it a bad idea to attach inside mounted blinds to side of trim?
I owned and operated a Budget Blinds franchise for two years.  As long as you comfortable with the support provided with you mount, you should be fine.  Cellular shades are so light.  The proper way to install them would be to mount L-brackets up through the window frame header and then window brackets to install the blind to the L-brackets.  If you call the company, they have a specialty bracket for you to use.