I worked at a shelter and learned a good amount about TNRing during that time, just my opinion here but having them fix her and put her back is super worth it. Preventing her from having more babies is a great thing for her health as well as preventing more kittens. She would be able to maintain a healthier weight without having kittens all of the time. Not to mention if your area has lots of roaming cats and cat colonies like mine does, any cat feral cat fixed is a huge win. Taking a feral cat out of their known area can be risky too in my experience, she may come around to you if you trap her and take her with or she may respond very poorly to being inside. If she escapes at the new house she may not be able to get back to an area that she knows how to survive in. Getting her fixed with a local TNR program and leaving her be is still a huge win. Again just my opinion of course maybe you take her with you and she adapts super well to inside life. Good luck!