In your circumstances i'd say it is always going to be difficult to move straight into a dispatch job.
Most companies i know would expect what they call " Flexibility " and i know from past experience that this is not always possible from working mums who have a hubby working full time.
That said i have known and still know of Feamle dispatchers with Kids and working hubbys however most of them have progressed through a company via Check in or even Cabin crew and have generally had their children whilst in dispatch and returned from Maternity leave to work Part Time.
In fact in a past company of mine we had 6 part timers all with youngsters but they had all progressed in the aforementioned way.
I think that most companies, interviewers, recruitment etc would be wary of taking someone in your circumstances straight into an ops department although one can never say never, i'd suggest the best course of action for yourself would be to start part time on check in and work your way into Dispatch via that route, growing into the job and hours as your children grow.
I guess this probably isn't the response you were hoping to hear, but i believe it is fairly close to the truth !
