From the facts presented in the question, it appears that you may qualify to enter the UK without a visa as a holder of an Article 10 or Article 20 residence card:
What you are allowed to do with a residence card
A valid Article 10 (or Article 20) residence card allows the non-EEA national family member of an EEA citizen to travel to the UK without the requirement to obtain an EEA or EU Settlement Scheme family permit.
However, in order to be admitted to the UK you will need to demonstrate that you have a right of admission under EU law. Without evidence that you have a right of admission, you will not be allowed to enter to the UK on the basis of your residence card.
The first thing you have to determine, though, is whether your card is in fact an Article 10 or 20 card. Since your wife is Belgian and you live in Belgium, there is a fairly good chance that it is not.
Article 10 or 20 residence card
An Article 10 residence card is a document which is issued under EU law (‘the Free Movement Directive’) by EEA Member States to non-EEA family members of EEA citizens who are exercising free movement rights in a Member State other than that of their nationality. For example, the non-EEA spouse of a French citizen who is living and working in Italy may be issued with an Article 10 residence card by the Italian authorities.
An Article 10 residence card should feature the wording “Residence Card of a Family Member of a Union Citizen”. Another document, “Permanent Residence Card of a Family Member of a Union Citizen” issued under Article 20 of the Directive is also acceptable.
Documents issued on any other basis, for example (biometric) residence permits issued under the national law of another Member State are not acceptable and do not exempt the holder from the requirement to obtain an EEA or EU Settlement Scheme (EUSS) family permit.
For example, a non-EEA spouse of a German citizen living in Germany will usually hold a residence permit issued under German domestic law. Therefore, a United Kingdom EEA family permit, or alternatively an EU Settlement Scheme family permit, is required for travel and entry to the UK.
A non-EEA spouse of a German citizen living and working in France will usually hold a residence card issued by the French authorities under EU law. Therefore, a United Kingdom issued family permit is not required for travel and entry to the UK.
If you are the non-EEA national family member of an EEA citizen and you do not hold a residence card issued under Article 10 or Article 20 by an EEA Member State, you will need to apply for an EEA or EU Settlement Scheme family permit before travelling to the UK with or to join your EEA family member.
To demonstrate the right of admission mentioned in the first quotation, you have to show (among other things) that your EU family member is either in the UK or traveling with you there. In this case, the EU family member is your wife, because it is not generally possible to derive a right of free movement from a sibling or dependent child. Because your wife is traveling with you that should be easy to prove.
You should bring a copy of your marriage certificate. You may not need to show it, but if the immigration officer insists on proof of the relationship the marriage certificate will be the best way to satisfy that demand.