I think if I were in your position, I would look to re-home the filly. She's got excellent bloodlines so you could market her as a ranch/cutting/sorting/working cow horse prospect and get a bit more money for her than just advertising her as an average filly.
I'm telling you, bloodlines like that will bring money, even in this crappy market.
Also, my experience with cutting bred horses like your filly, training them isn't for the faint of heart. They are quick and agile and energetic....and smart. Generally not the best combination for success when you don't have training experience. If you are truly interested in keeping the filly, I strongly suggest you involve a good trainer to help you with her. That way, you have the best chance of getting her broke enough to be safe with your kids, or the trainer will let you know if they don't believe she would be suitable for novice riders.
As for feeding, I don't generally believe in feeding sweet feed to anything. All of mine get nothing but good quality grass hay and fresh grass when there is some. They also have free access to a mineral block and they all stay fat and slick and healthy. Oh, and make sure you get the mineral lick designed for horses. Some that are designed for cattle have ingredients that can make a horse very sick or even kill it.