My ex-husband has asked me to promise never to remarry, for the children's sake. Must I comply?

No; once the iddah ends you are free to remarry, and your ex-husband has no right to stop it. His request may come from worry about the children, or from a sense of ownership he has not yet let go of. Listen to his concerns about the children, because some may be reasonable, such as who will live in the same house as them. Then reply calmly, for example: ‘I will put the children first in whatever I decide, but I cannot make promises about my future.’ If you remarry later, custody (hadhanah) rights may be affected, so get advice on that early. See remarrying.