How to setup domain and sub-domain to different hosting providers

Hello,

Current situation:

My domain: www.example.com which is with ‘BigRock’, which has nameservers connection to the ‘HostGator’. Now, I want to point www.blog.example.com sub-domain to ‘DigitalOcean’.

Expected output:

example.com (BigRock) ----> HostGator blog.example.com (BigRock) ----> DigitalOcean

In order to achieve this, following are the steps I have taken but it still doesn’t seem to be working as expected. I already waited for 48 hours after making these changes.

1. [In BigRock] Created the A record with the destination IP address of DigitalOcean droplet.
2. [DigitalOcean] Assigned the domain (sub-domain actually) to the DigitalOcean droplet (it has the A record inside it too).
3. [HostGator] Created (with Add a Domain option) a sub-domain inside HostGator (primary hosting connected via nameservers) which has A record that points to DigitalOcean.
4. [DigitalOcean] Since blog.example.com is a wordpress website, I changed the URLs inside it in the database.

I think step 1 and 2 are necessary, I’m not sure about step 3.

Can someone help me here please? I might not have provided all the necessary details so please feel free to ask any follow-up question. Thank you.