A lot depends on the age of the children and how much of the situation they can understand.
I would say weekly meetup too, but start with two hours, which would mean time for a meal plus some activity. Then build up to an afternoon. If there's a weekend sport or hobby they participate in maybe ex can go to that initially to cheer them on, or drop off/pick up.
Don't worry if you annoy exH and he threatens to go to court. Visitation is supposed to be about the best interests of the children and he would need to have the judge agree that whatever plan he has would fit that bill. The mediator should be emphasising the best interests of the children too.
My own visitation agreement called for the DCs staying with exH every other weekend, and that was going from being two parents under the same roof, so if your ex has barely seen the children for a good while he really can't expect the full on standard EOW (plus maybe a weeknight) -- he is a virtual stranger to them after all.
If he can't see the situation from their pov and seems to be insisting on his 'rights', then I would actually consult a social worker, if you can get the name of someone perhaps from the DCs' school, or see if the school or your GP can refer the DCs to a SW for assessment and for a recommendation.
Women's Aid might also be a good resource for you (0808 2000 247)