Thank you for your question. Please note that under the Just Answer policy and my licence governing Solicitors, I cannot provide specific advice on this forum.
I am presuming that your mother is British. The option to bring her husband is under Appendix FM spouse rule. In this application, your mother will have to show that she meets the financial requirement. As your mother is on pension and you state that she is limited funds , it could be a problem for her.
Please note that third party support is not allowed under the spouse application.
But I strongly suggest that you go to a qualified immigration solicitor to discuss this in more detail or explore other avenues. As your mother's husband is an American citizen he can stay in the uk for a maximum 6 months per year but he will not be allowed to stay in the uk permanently unless he qualifies for the spouse application.
Please kindly do forget to rate my answer.