Employers must release you and hold your job if you file for disability with them.
When my son was going to go to rehab I notified his HR department. Due to confidentiality laws they could not tell his boss why he was taking a leave but had to give him one.
You know that your job and kids will get by but right now your sobriety has to come first.
Don't be shy about asking for all the help you needs.
Don't worry about what to expect at rehab. Just be willing to go to whatever length necessary to get well. Be willing to follow directions. Let go and surrender to the process. You don't need to be in control.
Wishing you all the best as you take this gigantic step.