BigIQ: Need assistance building a script with API calls

I have been tasked with building a script that can pull data from BigIQ then output the data in a given format.

The goal of the script is to:

1. Gather all VIP's and their associated Pools
2. Within those pools, get info on their associated Members
3. Arrange the data (VIP, Pool, Pool Members) as needed, then output to file

I think I have a good grasp of 1, but with 2 I am having trouble referencing a specific pool (gathered in step 1) in the API so I can gather the Member data. In my research I found the URI to be

/mgmt/cm/adc-core/working-config/ltm/pool/{id}/members

, but it presents me with two problems:

1. I cannot figure out how to find out what the Pool

   {id}

   value is without first looking up the pool by name.
2. I do not know how to filter the results by Pool Name to collect that ID value. I found another resource that suggests I can append "?$filter=" like so:

   /mgmt/cm/adc-core/working-config/ltm/pool?$filter=name eq 'name-of-pool'

   but I always get the full table of all pools, not just the one with the given name in the filter.

I am running BigIQ 5.3.

Is anyone able to assist? Helpful links are good but I would prefer more direct assistance if possible.