You will need a confident, positive and no-nonsense attitude for a start - whether she is napping from insecurity, stubbornness or something else, she will take her cue from you! Don't be afraid to get off if her behaviour unnerves you - staying on and getting worried will probably exascerbate things - she needs to be moving forwards and in the direction you dictate, but it doesn't matter if you're doing it from the saddle or from the ground. Far better to lead her than to turn home, which will just make her think that was what you wanted.
When she naps, your responses need to be immediate - don't take time to think, and don't give HER time to think either! Then when you get what you want, give her lots of praise. It's not just about telling her off for doing something wrong but also making it clear when she's done something right.
When she spins around or turns away from the direction you were going in, make sure to turn her back the opposite way. So if she spun around to the left, turn her back to the right. If you circle left she'll think that turning left was OK (it wasn't, because you didn't ask for it). As you ask her to turn, hold your hands nice and wide, I find this gives you more influence over direction than when your hands are close together. Then when she's facing the way you want, praise her for it.
As soon as she's facing the right way and has been praised for it, ask her to go forwards. Start with a small amount of pressure and only increase it if you don't get a response. So try a quiet leg aid first, and if she moves forwards from that you can carry on your way. If the quiet leg doesn't get a response then try a good old fashioned Pony Club kick first. Failing that, back up your kick with a smack on the shoulder with your crop, and/or growling at her if she's the sort that reacts to the voice. If you still don't get forwards put the reins in one hand and give her a crack on the butt - but usually you will get a response before it gets this firm!
I always try to build up the pressure, because if you START with a mahoosive smack and don't get a response, where do you go from there. The only exception is when the horse's behaviour is putting us or others in immediate danger (eg. misbehaving in front of a car or running into someone on the ground) - in those situations my IMMEDIATE reaction is 3 very hard smacks on the backside along with a massive boot in the ribs and a lot of growling. I have to say this has always been successful in getting them back in control. Am not advocating "giving it a good beating" as a first response to dealing with napping, but sometimes you have to be harsh for your own safety. I always hack with either a crop or a schooling whip for this reason if nothing else.
That's how I do it anyway, it is personal preference of course! I don't deal with napping issues by going back a step and taking them in-hand / long-reining / getting a foot soldier - I prefer, and find it more effective, to just keep hacking out as normal and deal with the behaviour as and when it happens. IMO if your mare has been good to hack in the past then there's no need to "re-educate" her as she already knows what's required of her. To go long-lining or whatever I would consider to be a step back that you don't really need to take.