Hi camilla
Also, what would be the position with my husband, from whom I am separated? He is a Scientologist (part of the reason we split up) although he is still in mine and my daughter's lives on a part-time basis. I don't really want another relationship. Is it ok for a Muslim woman to live alone with her daughter indefinitely, or would I have to reunite with my husband, or divorce him and finsd a Muslim husband?
That is a very difficult question, since it involves many issues at once. I can't tell you what to do, you'll have to decide that for yourself. I can only say what I do know.
First of all, where you married to him? Secondly, if you were married did you divorce him, or are you officially still married, but just living separated? Obviously it seems only fair towards him and towards your daughter to not cut him out of your life altogether. But if you're divorced you should avoid being alone with him (in private) or having any physical contact. But obviously you would still have to meet him, like when your daughter goes to visit him and so on.
As for your question whether it's ok to stay alone. It is
recommended both for man and woman to marry when it is possible. It is said that marriage is half of the religion:
Prophet Muhammad (peace be upon him) declared:
"When the servant of Allah marries, he has fulfilled half the (responsibilities laid on him by the) faith; so let him be God conscious with respect to the other half". (Mishkat)
Marriage has also been commended as the way of the prophets:
"We indeed sent messengers before you (O Muhammad), and We assigned them wives and children" (Quran 13:38)
That being said, reuniting with your previous husband would not be permitted. It is not permitted for a muslimah to marry a non-muslim man. And obviously it wouldn't be justified to ask him to convert to Islam just for the sake of appearances.
But of course I can understand that you might have reservations, in terms. Perhaps due to fear for acceptance of your daughter or simply because you need some time to heal emotionally from your last relationship. Perhaps you need to take things day by day for a while and not worry to much about what the future will bring. Afterall, we can't predict what 'll happen eitherway. And it's not like you have a dead-line where you need to be married as soon as possible. Marriage is recommended, not obliged. Just keep an open mind to the possibility would be my advice. And Allah subhana wa ta'ala knows best.