DNS to direct url with path to another domain

Technically what you're asking for is invalid. CNAME conflicts with all other records (with a special exception for DNSSEC records), thus having CNAME xxxxx conflicts with the SOA, MX, NS etc records for the domain. My guess is that the reason the domain resolves when you use an A there and fails when you use CNAME is because the DNS server enforces those restrictions and is unable to process your zone file.

Furthermore, based on your response to @xwincftwx's question, it's not clear that getting CNAME to work would do what you want in the first place. A CNAME pointing to an A record is exactly the same as an A record in the first place. The CNAME is handled entirely internally by the DNS system and the web browser only sees the IP address. In your test with an A record (let's say 1.2.3.4), the browser connected to 1.2.3.4 and asked it for the website example.com. If that server isn't configured to serve a website for example.com it typically serves a default site (in this case blogs.com).

If you got your domain to work as a CNAME, the browser would ask for the IP address of example.com. DNS would see that it is a CNAME, look up example.blogs.com and return 1.2.3.4. The browser would connect to 1.2.3.4 and ask it for example.com just as it did when it was an A record.

If you want people going to example.com to be redirected to example.blogs.com then you'll need to set up a basic web server that receives connections to example.com and sends a 301 permanent redirect to the browser to tell it go to example.blogs.com

Check the DKIM signature in the header. The diagnostic messages seem to indicate that the domain field (d=) is empty or missing. Ensure you are supplying your domain when you sign the emails. The DKIM header should look something like the following:

DKIM-Signature: v=1; a=rsa-sha256; q=dns/txt; c=relaxed/relaxed;
    d=example.com; s=201602; h=Content-Transfer-Encoding:Content-Type:
    MIME-Version:Date:Message-ID:Subject:From:To;
    bh=GUIz2zzhMS1zh+o3BSEHOEq5KPzYRRlG+wqnc7+1vNM=; b=Q0LXbOPly2f1Ns6kpuS5e6dykT
    mefOZ8WX5tzNR0jD4Mqttg9IDutAE25M3FR+1UXcnakHCIsj+ELuoqafHvu/1av6vvAhZXMudoo/V
    wz3FDWwUnOroIaDPLvSR9RgBA/SHpPL9REEpCtN5WDnWDQK4P69CygrX+zbyh60aZVhE=;