Can an employer accomodite 2 employees sched. for childcare & deny 1 who has child w/diabetes?

I was working second shift & was asked by my employer to switch spots w/another employee & work mornings, now 3 months later the other employee wants mornings back for childcare reasons so they moved me back to nights. I called hr & explained i had child w/type 1 diabetes and my childcare arrangements currently have noone available to watch him except the daytime, they told me i could get fmla and talk to my mgr to see if he can accomodate my needs. So i explained to him the situation and he said hed see what he can do. Now i find out another person was given a set morning schedule to care for a grandchild after they were told they had to have open availability, so im wondering how i should handle this. And if i should contact an attorney or hr or what is the best action because its causing alot of stress etc with family/work balance. Thanks!