I am an ER doctor and STBX is an ICU nurse...
I am hoping that a new lawyer can at least get me every weekend and eventually 50-50 custody.
Courts almost always order alternate weekends for the non-primary parent in a temp order. (Some states are more willing to start with 50/50 in recent years.) I had that for two years during my separation and divorce process. No one including my lawyer seemed motivated to change that because it was only "temporary". Problem is, our cases take much longer to get to the final decree. So best to obtain the "least unfavorable" temp order.
Judges will make an exception if someone is a doctor, nurse, fireman, paramedic, etc who has to work regular weekends. If you are available on weekends while stbEx is working then that is a good argument to present to the court. What you may be looking for is some sort of
Right of First Refusal clause in your order where you get first option to parent if your stbEx is working.
Be aware that she will certainly try to weasel out of any reasonable terms. If it says you get the kids rather than grandparents or daycare if she works the weekend, then she'll claim she only works one day on the weekend. Or if you set the limit at any weekend over 7 hours then she'll claim her shift is only 6 hours.
We were ordered mediation yesterday, but my STBX if not just the mediation type.
Courts almost always order mediation as the first step after setting a temporary order. For us, it often fails because the stbEx feels so entitled so early in the case. The experience here is to try mediation but once it becomes clear the stbEx isn't really negotiating then declare it failed. Mediation is NOT the place where your stbEx sets the terms and you have to acquiesce.
Some states allow partial success to be reported to the court. Other states have mediation a black box for all or nothing results. Do you have an experienced proactive lawyer? Our best handbook for court is William Eddy's
Splitting: Protecting Yourself While Divorcing Someone with Borderline or Narcissistic Personality Disorder.
One last thought. She moved away some 5 hours. Federal law which states abide by is that a parent who moved away has to reside in that new state for at least 6 months before filing a custodial case there. Otherwise the residency is still back in the prior residence area. That would probably be in your favor? (If still the same state then you'd need a lawyer to advise whether her moving away intrastate puts you at an advantage.)