how does a 10 year visa ban affect a spousal visa

A UK "visa ban" is technically a "entry ban". This means you are forbidden from entering the UK, with or without a visa. Visa applications are automatically refused if you have an entry ban.

Spousal visas are visas, and are issued at the discretion of the UK. There is no "right" to a visa, even a spousal visa. Having a child also makes no difference.

There used to be a rule called "Surinder Singh" which meant that spouses of EU citizens could not be denied free movement within the EU. This rule no longer applies in the UK after 29 March 2022.

Your options are: a) wait out the ten year ban (although even then you might not be granted a visa) b) attempt to overturn the ban (requiring a good immigration lawyer and a lot of money, and not being guaranteed) c) relocate your family to a country where you have right of abode.

Under article 8 of the European Convention on Human Rights (ECHR), the right to private and family life is protected, which has been interpreted to include a right to family reunification. The UK remains bound to the Convention as a Council of Europe (distinct from the European Union) member and does consider such considerations when making a decision on immigration applications related to family members.

This means the automatic refusals under Immigration Rules for previous violations of immigration laws do not apply to applications under Appendix FM (Family Members).

Applicants applying as a partner or parent under Appendix FM to the Immigration Rules are not subject to the grounds for refusal, except in the limited categories set out in paragraph 9.1.1. of Part 9 of the Immigration Rules.

The exceptions to this general deference to article 8 rights are established in paragraph 9.1.1 which provides

9.1.1. Part 9 does not apply to the following:

(a) Appendix FM, except paragraphs 9.2.2, 9.3.2, 9.4.5, 9.9.2, 9.15.1, 9.15.2, 9.15.3, 9.16.2, 9.19.2, 9.20.1, 9.23.1 and 9.24.1. apply, and paragraph 9.7.3 applies to permission to stay; and paragraph 9.8.2 (a) and (c). applies where the application is for entry clearance; and [...]

covering mostly grounds related to criminality, lack of travel document, public health, refusal to cooperate with immigration officials, past and further breach of customs and immigration laws.

For past violations, paragraph 9.8.2 states:

9.8.2. An application for entry clearance or permission to enter may be refused where:

• (a) the applicant has previously breached immigration laws; and
• (b) the application was made outside the relevant time period in paragraph 9.8.7; and
• (c) the applicant has previously contrived in a significant way to frustrate the intention of the rules, or there are other aggravating circumstances (in addition to the immigration breach), such as a failure to cooperate with the redocumentation process, such as using a false identity, or a failure to comply with enforcement processes, such as failing to report, or absconding.

It is a discretionary power ("may") to refuse an application from an applicant with aggravating factors in their past violations. Specifically for FM applicants, item (b) does not apply which normally entails a mandatory automatic refusal for an application within a prescribed time period (e.g. 10 years for deception).

Your 10-year visa ban does not apply if you qualify as an applicant under the Partner/Parent category. However, this does not guarantee the acceptance of your application. If the past violation was a "simple" mistake or can be otherwise explained (while recognizing your fault), the human rights considerations may prevail. Otherwise, the UK reserves the right to nonetheless refuse applications where the applicant is considered undesirable or unreliable for reasons related to public safety and maintenance of integrity of their immigration system.