@Frillylilly, you have a really challenging situation on your hands! It can be transformed, but it sounds like a lot of work. To borrow an expression: you are working on what has been spoiled, but you can have supreme success.
One can kill Bermudagrass with Roundup most effectively in fall when the carbs are moving from leaf to stolons/roots for winter storage, although any time the leaves are green, one can have partial success. One year, I Roundupped in Sept/Oct to create flower beds and was surprised by how totally it worked on old bermuda lawn. But then... if one doesn't have buried edging or a physical barrier, it just creeps back, superficially and underground. Where I used 8" hammer-in edging, it stayed out of the beds and where I didn't... well... not so good. Bermudagrass is really hard to deal with once it's involved with plants. That's a whole different story.
