What determines if my command sponsorship will get approved or denied?

EFMP, Medical facilities, and housing availability.
Everyone is screened for EFMP, if your spouse has or had in previous years a medical issue that can affect whether or not EFMP is approved. For instance, they take medications, or they had a non cancerous tumor removed that has to be monitored in the future, or they once had mental health issues.
Whether or not there are EFMP issues, the medical facility must be able to accept a new patient. Or, if military medical isn't used, like in Belgium, if the local economy can support.
There has to be somewhere for spouses to live. E6 and below in most OCONUS assignments are required to live in government furnished housing. If there is not enough housing that is government furnished, or in the surrounding area, the family cannot go.

Usually if they have space where you are going or if they even have CS at the base you will be stationed at. Not all bases in Korea for example don’t have facilities for families to be there for two years. The other thing will be if you have a family member who is under the EFMP program. Certain overseas Basra’s won’t have the accommodations for a family member. I was not able to take my family with me this time to Korea because they didn’t have speech therapist for my son so my family stayed back in Colorado. You won’t really know until you send the request up and that place accepts of denies you.