Is the husband Islamically permitted to prevent his wife from living in her own house, which she built with her private funds, especially since she wishes to live in it with her children and desires for him to join them as well?

If you did not stipulate in the marriage contract with your husband that you would reside in your house, then he is not obliged to agree to that. Rather, he is obliged to provide you with an independent and suitable dwelling, and it is not a condition that the dwelling be owned by him. If you are unable to convince him to reside in your house, then you must obey him in living where he lives, as long as he provides suitable accommodation.