After reading a few of your responses to others geeks im going to suggest a different strategy.
You seem really determined to make this business succeed but for whatever reason your dad still wants to control and have final say.
With this in mind i would sit down as a family. Not just you and your dad but you, him, your mum and sister too and thrash it out. List everything you have done and want to do to try and improve the business and back up with sound reasoning ie recommend a friend will help gain more clients etc. Ask him why he drags his feet with things. With having your mum and sister there they should be able to support you.
You then have two options. Ask to be made ceo of the company as for reasons you have stated above you feel your dad isnt doing the business any favours and the business needs to be run differently. Offer to pay a set rate back each week so that your dad gets back his financial investment
Or secondly stick to being an employee but with that first and formost you wage goes up to minimum wage otherwise your dad is breaking the law and you only do set tasks and he has to do the rest such as marketing, accounts, handling complaints etc.
If niether of these situations suit your father then you need to be strong and say your walking away. But give it a chance first. He could just be trying to protect his little girl and he could also be feeling out of his depth with a business he has no experience of running and is scared it will fail. By the sounds of it he has down the usual man thing of hiding in his cave and hoping everything will come up rosy when that most certainly doesnt happen.
Be kind and ask him why he is doing things as he is and point out where improvements could be made. Show him your a team and want him to get the most out of his investment. My grandma has an amazing skill of of telling my grandad of what needs doing and how he needs to do it but she always lets him think it was all his idea, keeps everyone happy without anyone being manipulated. Think you need to work on this with your dad so you both get the best out of the business.
If on the other hand as vic said and its all down to control and he wont hear any of it then its time to down tools and back away. Get yourself set up somewhere else asap and forget the three months notice, just go cos if he is that controlling with work what else is he controlling about?
Sorry this is a long post but i think this is the route you need to be taking before you can be doing anything to improve the business. Hope it all works out for the best which ever direction you end up taking.
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Thank you so much ladies. I'm really touched by this heart felt approached. He loves me dearly and is trying to set me up financially for the future. I feel there are too many difference in opinions. I'm sure if made a list that included suggestions, costs, negatives & positives he would listen but he takes so long as everything costs money which we don't have apparently. I'm frustrated because I feel that if we can't afford it maybe we should set deadlines and maybe save towards them.
I think he's reluctant because he's a frugal man and doesn't believe in throwing money at things, therefore he likes to take months to consider whether or not something is a worthy investment.
I live with him but until I get minimum wage I can't afford living costs.
I'm sick of living under my parents , I want to spread my wings.
How do other businesses cope when they can't afford to make ends meet? I doubt they pay their staff below minimum wage.
My parents feel like I've thrown everything back in their face. They set this business up so me and my sister would be financial stable but my sister was working for them for 4years and was on £1.50 an hour as was I until she left.
I'm a lone worker and he doesn't see the point in hiring somebody if there usually isn't enough work for 2hands but then I don't think a beautician should be leaving a customer with her bits out during a hollywood wax to constantly answer the phone and serve Sunbed clients.
I think it would be a while before the business would be making enough to pay me a full wage. He thinks it won't be long.
But I have no idea what the finances are, it's not a secret but he doesn't openly discuss it and he can't rattle off his head the figures. Which I think a business owner should know like the back of their hand