The Law Society of British Columbia is the organization which regulates people practicing as lawyers in the province. Under the Legal Profession Act, the Law Society is also responsible for licensing lawyers, which gives it the collateral authority to take action against those who perform legal services but aren't licensed to do so.
When the Law Society runs into someone engaging in the "unauthorized" practice law, it usually applies to court for an injunction prohibiting the person from practicing law for a fee or representing him- or herself as a lawyer. The Law Society issues regular press releases summarizing its activities in this regard, such as its press release from 1 November 2013 which identifies five people who have been restrained from practicing law.
To find out whether the person you are thinking of retaining or have retained! is a lawyer, you should check the Lawyer Lookup tool on the Law Society's website or call the Law Society at 604-669-2533 or 800-903-5300. Or, you could take the opposite approach and see whether the person is listed in the Law Society's database of unauthorized practitioners. If you're hiring a lawyer to represent you in a family law matter, it makes sense that you'd want to make sure that the lawyer has the right training and knowledge and is approved by the Law Society to do so.
If it turns out that the person representing you isn't licensed to practice in British Columbia, you should terminate his or her services right away and hire a real lawyer. You do not want to have your legal position damaged by the advice or actions of someone who doesn't have the right knowledge, skills or training. You should also contact the Law Society and let it know what has happened to you.
As a footnote, since you're hiring someone to represent you with one of the most important problems you will ever have to deal with, you can go further and check the Law Society's hearing reports and admissions database, which identifies lawyers who have been formally cited by the Law Society for violations of its rules or code of conduct. The current citations and hearings page shows the status of all current citations and related disciplinary proceedings.