I would think the translated copy would be sufficient for a visa from London but someone more qualified than me, should confirm. I needed mine legalised and certified for an Extension applied for in Thailand.
Make sure your marriage certificate has been legalised in the country where you married and then certified by the Thai Embassy in that country. If the certificate is not in English it will also need to be translated.
if you're just staying here on holiday. However if you plan on a lengthy stay and if the child is likely to be educated here, I think it's better to remain legal.
As Biff says, there are no fines or bans for under-15s who overstay. They do get an overstay stamp in their passport though. If the baby will be living long-term in Thailand it might be better to legal but if it's short-term as you plan to settle in the UK (or Cambodia?) it's unlikely to be an issue.
While a pain, it does work quite efficiently. Just make sure you include a pre-paid envelope addressed to the Thai Embassy in London (for the Legalisation Office to use) and a pre-paid envelope addressed to you for the Thai Embassy to send the document back. The Legalisation fee is paid online, but when I did it, the Thai Embassy insisted on a £10 postal order. The whole process took around 2 weeks. It helps if you can do it all within the UK.
Everything is detailed on the website. If she has a job or definite reason to return to Thailand, getting a visitor visa is straightforward. If she has her own money and can prove she can pay for the whole trip it's easy. Loads of Thais visit the UK as tourists. If you are sponsoring her (i.e paying for the trip) you will need to show you can do this.
I've had friends on Ed visas for studying French, Japanese, any university degree, Muay Thai. All depends on whether the school/course meets the requirements.