As you have limitations to the manuverability of your mower - how big or small - I like to stringtrim around trees, posts, birdbaths, flowerbeds, in corners, etc. prior to mowing, therefore I can pickup all those clippings too with the mower.
The other reason for trimming first is:- if I let the mower operator mow first he/she is usually leaving bigger areas to stringtrim and that is frustating, time consuming and hard on both the stringtrimmer and the grass or he/she is going to try and trim with the mower leaving tire tracks around all those obstacles.
My advise is - and it works for me - let your stringtrim operator know the limitations to the manuverability of the mower he is working with and have him stringtrim only where the mower cannot reach and then let the mower do the rest of the work for you.
Your trimming job is going to determine how good your overall mowing job is going to look like.
Once you're done then blow and clean off the drives and walks.
PC & N Services
It's your lawn, It's our talent
I use Gopher Billing & Scheduling Software.
Download your FREE fully functional 30-day trial here.