Hiya hun
(((hugs))) for the EW. I have truly been there. My DS has also been an EW'er for most of his life.
When he's at home with you, what time does he take his second nap? And did I read right that he takes 45mins nap in the morning & 2hrs in the afternoon on the days he's at home?
How many days is he at the CM each week?
Well hun, there's no easy answer to dealing with this. I think he probably needs rid of the morning nap that you are giving him at home at 8am. One of the biggest causes of EW can be offering a too early & too long morning nap. His is most definitely too early. And trust me I know exactly why you do it, b/c he is tired from waking early. I did the very same thing with my DS. But unfortunately, offering the nap early will mean he can use that morning nap to catch up on what he missed at night, & he will therefore continue to wake early.
However, pushing him straight to 1 nap from a 4-4.30am WU will be very very difficult for him b/c that's a really long time to expect him to stay awake. I expect this is why he's only napping for 1hr with the CM - b/c he's waaay overtired by naptime. Getting OT like this can in itself cause EW too.
If you can answer my questions I think I can help you with a plan. I have done this & it is not easy, but it does work.
It involves pushing that AM nap gradually later, & shortening it, until it is just a short 10min catnap at around 10am, which will help him last until his big nap in the afternoon. This should help to bring his wakeup a bit later, which in turn should help you to drop the AM nap completely. In the mean time, on days at the CM, would she agree to doing a very short CN in the AM (say in the pushchair if she has activities to go to?) so he has a consistent routine all week? Or if she can't do the CN could she put him down for his nap a bit earlier say 11.30-12? Again if she can't & he does a short nap of less than 2hrs then early bedtime is always a good idea to help prevent OT. At the moment he is going to bed at 7pm & waking at 4-4.30. If he only naps 1hr at CM's & you put him to bed at 6 or 6.30, ok, he may still wake at 4-4.30am but he'll have had 1hrs extra sleep IYSWIM? Or he might surprise you & sleep for longer. I know my DS will often do his longest nights after an early bedtime.