So,you would 'give' him permission in 'particular circumstances'...but you would not like him to have children with his second wife. Well,what if she wants wants them....isn't it natural for a woman to want to have her husbands children?...what if the 'widow' or 'divorcee' does not have kids of her own.Isn't that like placing a condition on the relationship? A man does not **have to have more than one wife....**if she is unbearable then just leave her...otherwise have a fulfilling life with the one wife. Lord...what is it with men and 'more than one wife'....
There are plenty of women who don't want to have kids of their own.
People remarry for different reasons, some aren't happy with their wives, some want kids and can't have them with the first wife and some people remarry just to give a poor and week woman security and honour.
I'd let him marry for a woman just for the sake of helping her and honoring her otherwise there's no reason that I could agree to it. If she wants kids then I'm sorry, I'll have to say no to their marriage.