Big John, not sure if you got this settled yet, but if not PM me and we can talk.
I went through this for 3 years, plus my undergrad and BS is in PreLaw so I have some solid experience in this area. It will depend on the State and age of the kids and supervision. If you are the sole parent in the house then yes, they would want to change the custody status, however it could be "temporary" until you find another job, you can put that into the order but if this is the case, you may be better off collecting unemployment and finding a job that suits your current custody agreement.
Also,If you have a "new" wife and she is home, or you have one of the "grandparents" of the children available that has a relationship with the kids, it very well may count as "supervision" depending on her length of time in the residence and also dependent if you have a "first refusal" clause in your custody arrangement.
First refusal means that should you need babysitting or supervision of your children, the custody agreement would make it clear that both you and your Ex would have to contact the other parent FIRST and foremost and give you the opportunity to watch the children prior to hiring a babysitter, daycare, etc...
But this would have to be written specifically into the agreement.
All custody agreements can change and be changed. Good luck and again PM me if you need to discuss options
