In all honesty, it takes years for a horse to turn up as a solid, proven and consistent barrel horse. After around eight months, the horse will probably know the pattern... but it will take lots of time for the horse to be that solid barrel horse. I have a mare who I race that is also fourteen. She's foaled one time. Other than her "maternity leave" she's been running barrels since she was three years old.
Take it easy on the mare, as she is older than most all starting barrel horses usually are. After having foaled twice, she could possibly be out of shape. Try taking her off the pattern for a couple of weeks and do some simple exercises. Begin with walking her for 15-30 minutes. It is hot this time of year, so go easy on her. After walking do some long trotting. It builds muscle. You could also trot her up hills some. Not big mountains, but just small hills that aren't inclined too much - if they're available where you're at. After doing that for a week or so, lope her some... but work up to the lope. Walk for a while, trot for a while then kick her up into a lope. Loping also builds lung capacity which is needed in the intense world of barrel racing.
There's also a couple other exercises that I do with my barrel horses. I often set out one barrel in the middle of the arena and then set out four tires around the barrel. Set them about 8 feet from the barrel in a diamond shape. If no tires are available use cones or even buckets. Start at a trot and trot the horse around the tires without turning them like you would a barrel. Every once in a while turn the horse around the tire (or what ever you're using) and keep her picked up and don't let her break her trot. Do this at a lope later. I read this one out of a Barrel Horse magazine (get a subscription to them, they often have nice exercises in them and have wonderful places to buy nice tack!)
You can also do some exercises that I heard about by watching Fallon Taylor on YouTube. (Look her up, she often uploads videos with tips for training barrel horses.) She has one that I use a LOT. It's probably the most simple thing ever too. Just walk/trot/lope the horse in a figure 8 pattern. You also use a lot of neck reining, which can really help in the barrel racing world. When you turn, switch hands into the direction you are going, and when you turn, put your leg into her and use one hand to turn her. Easy!
One more that came from Fallon... it's also really easy. It's all about adding speed also. If you have an arena or dirt track (don't do this on grass or you risk the horse falling and getting hurt... or hurting yourself!) work the horse up from a walk, to a trot to a lope... then let her loose. You can kick or whatever you like. Just let her run her heart out until you feel like she's slowing down. Then take around 25 minutes to cool her down... back into a lope, then a trot, then a walk. Just do this until the horse is breathing normally again.
There are tons and tons of exercises for barrel horses that have nothing to do with the pattern. But it is all about slow work. Don't run the horse every time you get on her, in fact, don't run her at all. If you do that, she'll become sour and won't run it. She'll hate it! Do these exercises, get the horse into great shape and then do it some, but don't over do it. Keep it slow more than 95% of the time. Once the horse knows the pattern, don't put her on it but maybe a couple times a month.