I'm really sorry to hear this Monkas.
I know a few adults that still choose to keep their cats even when they have asthma. There are sprays and pumps that can help deal with the symptoms.
I don't have children - so I do not know what i would do in your situation. I guess it would depend on how bad the asthma is and in what situations do "attacks" happen. Is this asthma new? how often are the attacks? does something specific trigger the attack? Are some attacks more severe than others?
If I did have children and the asthma was severe enough that i had to "make a choice" , as much as I love animals, the animals would lose..... but maybe the answers to some of the questions might spark some ideas for other members. maybe increased bathing and brushing and restricting their access to certain rooms can help.... just throwing out possibilities.
Please know that as much as we want to help, pets cannot be posted for adoption on this forum. Of course you are free to PM those members in rescue that may have leads for you.
I hope members have additional suggestions for you