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My husband owns the house and we are legally married although living separate and apart in the house for just over a year.
If you are legally married, then you have as much right to use and access the family home as he does. That means you have the right to invite your mother into your home, and your spouse has no legal ability to refuse or deny her entry.
You also both have legal joint custody, and so one parent has no legal ability to override parenting decisions of the other. If he is not going to be present, such as when he leaves for work, if you want to leave the children in the care of your mother, then there is nothing he can do to prevent that. Certainly while he is at home he would be entitled to keep the children in his care as opposed to your mother's.
If he is taking steps such as locking you or your mother out of the home, or being abusive, or interfering with her ability to care for the children in his absence, you can apply to a family court judge to seek an order be put in place that can clearly define what rights each of you have with respect to use of the home, and parenting of the children, and what third party can care for the children if each of you are at work.