All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
You were not clear whether your husband is a Muslim or not? If he is not Muslim, then you are not lawful for him after accepting Islam. You are not allowed to let him enjoy you, and you must separate from him.
If he is Muslim, as expected, and discord occurred as you mentioned, then we advise you to be patient, try your best to reach a settlement and supplicate Allaah as much as possible to bring peace and love between you and your husband. Remind him that he will get a great reward for being kind to your mother even if it is not obligatory upon him. You have to express your gratitude to your husband clearly and frankly for his support and you have to supplicate for him in front of him and in his absence. Tell him that you are supplicating for him for his help. These are some methods that may make him tenderhearted and you may also use other suitable methods. We supplicate Allaah to help you make your husband affectionate for you, and for Allaah to satisfy you with His bliss. You may ask those who can influence your husband to talk to and to exhort him.
Know that basically your husband is not obliged to make your mother or your child to live in his house. However, if you made that a condition prior to your marriage and he accepted it then he has to fulfill his promise except if there is harm in letting them live in his house; then he may prevent them from living there.
If your husband insists on his refusal, then it is better for you to rent a separate accommodation for your mother near your location, if it is possible, so that you may visit her or she may visit you. It is also preferable to hire a maid for her if she needs one. In any case, you must not leave her alone if she cannot serve herself and does not have any one who can care for her even if your husband does not approve of it.
Allaah Knows best.