If there is a restraining order against the father during a divorce what are his visiting options/rules?

Depends on the terms of the restraining order and the reasons for it. Also ANY question on law needs to include your general locale as laws vary by area.

Is the restraining order merely against the ex ? If so, they either arrange handing off the kids at the local police station or fire house, ( common) or they arrange for a third party to pick up and drop off the kids at each others location

You need to read the restraining order and if you don't understand the language in it take it to a lawyer that can explain it to you in plain english.

As has been said the extent of the order is based on the nature of the offense that created it.

An order of restraint for verbal abuse wouldn't have the same weight as an order that was created because of physical violence.

Read the order carefully.