Your post did make sense except did you talk to the lady you were supposed to call back for? Is that the one that didn't know about vaccines?
If you think Lilly needs to have singles because you don't want all of them in the combo, then by all means insist on it. When Ellie's distemper titer was low, the vet said she thought they could get it in singles and did just that. She didn't debate with me for 10 minutes why I should use a combo.
If your other vet is someone you trust, I would most definately go back to them. You can protect Lilly if you are there with her at this place but your money is supporting them and sometimes there are emergencies after vaccines. Which vet would you rather see her then? In the back of the office without you... Please go to someone that you trust.