In reply to:
1. through my registrar, I change the dns records to point to dnsmadeeasy
You should directly point to DH.
In reply to:
4. I also purchase their email dns services and point to dreamhost.
You don't have to. DH has email server.
I don't think this will ensure that your website and email do onot go down. Once you point the DNS to Dreamhost, DH is the place to hold your website and emails. If DH goes down, dnsmadeeasy can't help because the website and email are in DH.
If you are not confident with DH's email server, you should point DNS to dnsmadeeasy and use its email server.
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