There is never a 'best' time, I'd say its the time that may have the least impact on kids, ie not just before a birthday/christmas. How old are the children? From experience, I believe it is easier on them the younger they are as they grow up and adapt.
Have you tried mediation/counselling? If he won't talk then your only option is probably to issue a petition. What grounds to you have? In absence of any adultery (that he'd need to admit) it will probably be unreasonable behaviour. Its relatively easy to get a petition together on that.
Whilst you are still living under the same roof the statement of arrangements for children form (a document that you must complete and issue with the divorce petition) will reflect that you are all still living under the same roof but that things will change at some point in the future.
Once you issue a petition it normally takes the Court a few days to issue it and they will send it to the Respondent (your husband). Normally its best to try to agree the contents of the petition but a bit hard if he has ostrich syndrome.
Feel like I need a divorce but want to know if there is a best age forkids. Also tried to talk to husband but not interested so looks like I have to get a divorce petition. When does the letter arrive? and what do I do about living arrangements?