Hi, thank you for your query.
I will try and assist as much as possible.
Under the Tier 4 student visa, your daughter is a allowed to bring a dependent. However, as you are aware, a parent does not count.
You have also rightly stated that as a visitor that your wife cannot stay in the UK for more than six months. If your wife wants to stay in the UK for longer than six months, then she could consider the following applications:
Tier 1 Entreprenuer- your wife will have set up a business and invest £200,000 in the UK
Tier 2 Work permit- Your wife can work in the UK as long as there is someone who is willing to sponsor.
Tier 4 student
Representative of an Overseas Business visa
Your other option is, but I would suggest not to pursue, is when your wife is in the UK, she can make a formal application to the Home Office under FLR (O) and request the Home Office to give your wife leave to remain to coincide with your daughter's term time. But, the prospect of this application succeeding is very low, and it may affect your wife's future visit visa applications.
Please do let me know if you have any further questions.