Living in the Republic of Ireland on British Passport, want to travel to England for weekend with South African passport holding family

In the event of a no-deal Brexit, free movement rules will remain in place until December 31, 2020, at least (possibly longer if the UK leaves the EU under the terms of a withdrawal agreement). They may be modified somewhat, however. I have not been able to find any draft legislation to change them, but the government has been making some fairly vague assertions about changes that are in store. Therefore, unless you're planning a weekend trip for 2021 or later, it is quite possible that your family members will be able to travel there with the EU family card and no UK visa.

The gov.uk page on this says:

Third country family members accompanying EU citizens

EU citizens who move to the UK after 31 October 2019 may be accompanied by their non-EU citizen family members. This includes direct family members (such as a spouse, civil partner or child), and extended family members (durable partners and dependent relatives), as now. They will need to be in possession of a valid national passport and an EEA family permit and will be able to stay in the UK until the end of 2020.

This also applies to short-term visitors. I suspect that the author(s) of this page simply forgot to consider the case of third-country family members who are in possession of Article 10 cards, so whether the Article 10 cards continue to be valid will depend on the changes that are made to the The Immigration (European Economic Area) Regulations 2016, if any, between the exit date and your trip.

Based on this Get ready for Brexit: check what you need to do - GOV.UK form
(which does not ask if a spouse is UK Citizen) :

Based on your answers, we know:

You do not own or operate a business or organisation
You are not an EU or British national
You live in Ireland
You plan to travel to the UK

returns:

You and your family
Take out appropriate travel insurance with health cover before travelling to the UK

You will be charged for your care if you do not have the right insurance.

Read the guidance: Healthcare after Brexit: citizens of the EU, Norway, Iceland, Liechtenstein and Switzerland visiting the UK

Do it as soon as possible

The same results turn up for non Irish EU-Citizens

• independent of whether they live and work in Ireland or in another EU Country

For Irish Citizens nothing has changed

• independent of whether they live and work in Ireland or in another EU Country

Ireland Information note on non-EEA family member of British citizens seeking EU Treaty Rights

If you are the holder of a valid Stamp 4 EUFam card
who is currently entitled to avail of the European Communities (Free Movement of Persons) Regulations 2015, you should have no concerns regarding your continued residence in Ireland after the 31 October 2019 (unless the draft Withdrawal Agreement is ratified before then). In a no-deal scenario you will no longer be subject to the provisions of the Free Movement Directive and the exercise of EU Treaty rights and entitlements. However, arrangements are being put in place for non-EU/EEA family members of British citizens who have been exercising Free Movement rights here up to 31 October 2019 to facilitate their transfer under domestic immigration arrangements to provide for their continued residence in the State. Insofar as possible, the objective is to retain similar rights to those that you would have enjoyed as a family member of an EU national including access to the labour market.

Family members of British citizens existing Stamp 4 EUFam card will be automatically converted to a corresponding normal Irish Residence Permit.

If we are reading the Common Travel Area (Version 5 from 4th September 2019) pdf corrrectly, holders of normal Irish Residence Permits does not automatically allow short visits (up to 3 months) to the UK from Ireland.

Citizens of South Africa and others that normally needed a UK visa, should contact the British Embassy for information on what is exactly needed.

Assume that a appropriate travel insurance with health coverage will be needed.