Only you can make that decision. Endeavour can help by fostering your pet while you are in the refuge – but inevitably some women will decide that it is better all round if they find their pet a new home. Giving up a beloved pet is sad; but realising that a pet is safe and happy in a new home can make the decision to leave a violent situation easier.
Your local animal rescue centre might be able to find a permanent home for your pet. Try to give them as much information about its background, behaviour, likes and dislikes as you can.
If you decide this is for the best, you may want to take some photographs of your pet for you and your children to keep.