In addition, choose an affinity for the source of your divine power: good, evil, law, chaos, or neutrality. You learn an additional spell based on that affinity, as shown below. It is a sorcerer spell for you, but it doesn't count against your number of sorcerer spells known. If you later replace this spell, you must replace it with a spell from the cleric spell list.

However, the feature doesn't incorporate it into my spells *known*, so I can't actually replace it and learn a new spell to go beyond my 10 known 1st level or higher spells.

How to work around this?

You can implement a simple workaround for it yourself fairly easily using the Homebrewer. (It'll take less than 5 minutes with a slow internet connection.):

1. Go here and copy the introductory description for the subclass: https://www.dndbeyond.com/classes/sorcerer#DivineSoul
2. Go here and create a Sorcerer subclass using the original Divine Soul as the template: https://www.dndbeyond.com/homebrew/creations/create-subclass
3. Paste the subclass' intro into both the Description and Short Description fields, and select “Cleric” in the dropdown labeled “Additional Spell List,” then [SAVE CHANGES].
4. Click “Edit” for the Divine Magic feature.
5. Where it shows that feature has the 5 initial Options, [ADD AN OPTION].
6. Name the Option something like "Affinity Spell Replacement;" in the Description field enter something similar to the suggested text below; set the Required Class Level to "2;" [CREATE OPTION].
    •  "Whenever you gain a sorcerer level you can choose one sorcerer spells you know and replace it. If you choose your affinity spell for replacement, you must replace it with a spell from the cleric spell list and of a level for which you have spell slots."
7. In the "Spells" section of your new Option, [ADD A SPELL]. Only enter the following information in the designated fields/dropdowns and completely ignore absolutely everything else:
    •  Spell Class: Cleric
    •  Level Divisor: 2
    •  Consumes Spell Slot: Yes
    •  Counts As Known: No
    •  [SAVE]
8. Then [SAVE CHANGES] for the Option, followed by the Feature, and finally for the whole Subclass.
9. Do anything you wish to kill the next 20 minutes, and then check your results on a character sheet.

Fin

Come back here and lemme know if there are any issues.

You can implement a simple workaround for it yourself fairly easily using the Homebrewer. (It'll take less than 5 minutes with a slow internet connection.):

1. Go here and copy the introductory description for the subclass: https://www.dndbeyond.com/classes/sorcerer#DivineSoul
2. Go here and create a Sorcerer subclass using the original Divine Soul as the template: https://www.dndbeyond.com/homebrew/creations/create-subclass
3. Paste the subclass' intro into both the Description and Short Description fields, and select “Cleric” in the dropdown labeled “Additional Spell List,” then [SAVE CHANGES].
4. Click “Edit” for the Divine Magic feature.
5. Where it shows that feature has the 5 initial Options, [ADD AN OPTION].
6. Name the Option something like "Affinity Spell Replacement;" in the Description field enter something similar to the suggested text below; set the Required Class Level to "2;" [CREATE OPTION].
    •  "Whenever you gain a sorcerer level you can choose one sorcerer spells you know and replace it. If you choose your affinity spell for replacement, you must replace it with a spell from the cleric spell list and of a level for which you have spell slots."
7. In the "Spells" section of your new Option, [ADD A SPELL]. Only enter the following information in the designated fields/dropdowns and complexly ignore absolutely everything else:
    •  Spell Class: Cleric
    •  Level Divisor: 2
    •  Consumes Spell Slot: Yes
    •  Counts As Known: No
    •  [SAVE]
8. Then [SAVE CHANGES] for the Option, followed by the Feature, and finally for the whole Subclass.
9. Do anything you wish to kill the next 20 minutes, and then check your results on a character sheet.

Followed this to the letter but it didn't yield any results.

When I go to the option in the builder to select Affinity Spell Replacement as my Divine Magic option, DnDBeyond doesn't register that I've made a choice, continuing to show a "!" next to the feature's title. 

I’m not entirely sure what is going on. If you followed those instructions exactly then it should be working perfectly. I know it works because another user tested it on YouTube.

All I can think of is:

1. You might have inadvertently clicked something else when adding the spell or when adding the Option.
2. DDB is working on something on the back end which is screwing something up.

 Can you please share screencaps of the Homebrew and the character builder? That will help rule out of locate any potential mistake on your part.