If you want a lift, the easiest thing to do is to purchase new coil springs and shocks, then take them to the shop and tell them "hey, my old coil springs are sagging, and my shocks are worn out" and ask them to install these new coil springs and shocks that you got. If the front struts are still OK, you can re-use them, but if they're tired and worn, you should replace them with the springs, since the labor to replace the spring is the same as to replace the strut, too. You don't have to tell them that your new parts provide any significant lift. The shop you used simply isn't familiar with suspension lifts for MacPherson strut-based IFS.
The only thing I have run into is that some shops refuse to install customer-supplied parts due to liability/warranty-claim issues.
After the springs are installed, of course, you should get an alignment. Camber bolts (which usually correct for positive camber after lifting) may or may not be required, but the toe angle will be off.
Also, with any lift, the front CV axles will be at a higher angle and could accelerate wear on the CV boots, and may potentially introduce mild vibration of the CV joints. If you want to mitigate these issues post-lift-install, you may consider installing manually hubs on the front wheels to disengage the front drivetrain while you're not using 4WD.