I hope someone else will advise you on this because I have no experience of it personally... just expressing some thoughts that come to mind... I don't think the British Embassy would check to see if she really had any kids if she said she had none on the application form? I'm just a little concerned about what might happen in the future if, say, she decided she wanted her son to join you in the UK...
The reason I asked about her age is that you said she was "quite young": just wondering if she was under 18 when she got the Birth Certificate i.e. below the age of marriage.
