I doubt she has planning consent for her business, as a neighbor who is affected by it you'd have been given the option to voice your concerns. I have a property adjacent to a school, when they needed to carry out extensive building works the standard letter arrived giving the timeline and place to raise objections along with your resons. If you've had no letter, I'd suggest she hasn't applied for the planning consent she would need to run a business from home. If you Google your town name and planning applications, you should be able to find out if she's applied for planning or not and whether it's been granted.
She may also not be declaring her income or paying taxes. If you want her to face consequences and possibly close down, a phone call to HMRC may help.
You could go down the route of approaching her customers directly and telling them they've no rights of access and to leave. Whether they turn round and leave or shout at you or whatever, if you make it less pleasant for them to use this hairdresser by politely challenging them, they may take their custom elsewhere.
Or she may start letting them in through her house, then it won't affect you so much. She probably doesn't want to do this for several reasons. Nobody wants endless people tramping dirt in from outside, seeing where/how they live and what they own, striking up friendships with their DC or bringing friends/family with them who end up sitting on the sofa while the hair appointment goes ahead, all of which is avoided if they don't set foot in the house to begin with.
There's also the issue of keeping what she's doing quiet. If lots of neighbors in the street start to see all and sundry entering/exiting her house at the front they're going to realise where the recent excess cars parking, which may be causing them an issue, has originated from. She'd probably rather have only one disgruntled neighbor (you) to deal with than all the street. Talk to others in the street to see if they'll put in complaints too, maybe it'll make it less likely she'd get retrospective planning consent if she's pissed off half the neighborhood.
People needing to earn a living doesn't mean they have the right to trample over other's rights to a quiet life in order to do so. She could be a mobile hairdresser travelling to client's homes to do it instead.