You can use both a Dymo Labelwriter(s) and Brother QL-710w(s) on the same check-in system.
There are a couple things to keep in mind:
Dymo Labelwriters can be used for:
Desktop Check-in (30256 & 30334 labels)
Mobile CheckIn Print Queue (30256 & 30334 labels)
Brother QL-710w can be used for:
Mobile CheckIn Print Queue (62mm x 100mm labels)
If you want to run both types of printers at the same time, your Check-in Setup tag setup must be set to either Large Shipping Label or Custom since the Brother QL-710w does not support the small label format of 30334.