how long had you worked and what is your skill level ?

Point no. 1: Ignore anybody here who has told you pole.
Really, I don't understand why people are telling you pole!
What you have is that someone has shoved under your very nose a great opportunity - and KShs 500k capital plus your lots of experience - to start your life all over again and some folks are telling you pole?! Ignore them.

The 'stress' you are feeling is normal and is nothing more than the feeling of being pushed out of your comfort zone ('guaranteed' regular income every month end) and seeking a new stable equilibrium.

Point 2: I know so many people who left salaried employment, started a business in which their core competence/ interest lay and they went on to establish very successful business empires. Remember that mama Milly who bakes cakes?
Some folks didn't wait to be retrenched - they just had the guts to quit!Others like you may have over the years entertained the idea of going into their businesses but never really had the guts to take the plunge - UNTIL they were let go by their employers. You belong to the latter category, ndugu.
Your competency is in cars/ motor. You are lucky because this is a going business/idea and like a working car all you have to do now is kuweka mafuta/ fuel it and off you zoom.
Why not invest in this business? Which cars to specialiase in? Say start a garage? Where to situate it? What is your vision about this garage: you running it, with competent mechanics, fair charges, specialising in a particular model, with an eating place where your customers (who will include your ex-employer's cars because you have not burnt your bridges)can have a bite as they wait for their cars to be fixed? etc. the options are endless and you will refine them with time.

Tell you what mate, start this garage and kindly give me the privilege of being your first customer to bring my car for service.

@McDreamy, you will be surprised how this may be a blessing in disguise, most of the things that people do on the side are what they are really tuned for and most never realize that,you say you are a part time mechanic,imagine what you would do with that skill now that you have the time.Market your services to your extended family and more-so former workmates and general colleagues and do them a good job.You will be shocked at the kind of business you can do with that skill you have.Most car owners know nothing about motoring and MVM issues,they are simply drivers.I have a feeling you can exploit that skill to the extent that you will be wondering why you ever looked for employment in the first place,many have done it and are doing it,it's an advantage also that your partner is still raising some income.

I support the idea that you cut the costs immediately, there is so much you can do in relation to that as you have been advised.Do not live a financial life to impress people,it will be catastrophic when the money runs out.So take serious measures to reduce your costs.

You also need to train your kids that there is no constant in life, we all want the best for them but the reality in life is that shit happens, we shouldn't shield them from that reality.There are a lot of good and reputable pocket friendly schools if you look keenly.Move your kids to one of these where the change will not be so drastic unlike moving them to a school in shags etc.Younger Kids have a way of adjusting to these changes.When things improve then you can re-assess and move them to a better school of your choice.Ensure you communicate and tell them why this is happening in a subtle but clear way, try to be open with them.

I have a feeling you will go far with the skills even as you send out CV's to potential employers, just have an open mind as a job may not appear when you need it and also stick to and do the obvious i.e. what is in the interest of your family.

The first and most important person to take care of now is YOU. Take one or two days and completely shut down the stressful experience. think about nothing but relax imagine everything is OK. Enjoy the freedom of not having to wake up and rush to work. After that (strictly one or two days) start planning your next move. Kids are stronger than we imagine so talk to them and prepare them for change. Look for a job or start one. Let me tell you my story. I was in the US doing a good job then some family tragedy hit me in Kenya. When my contract came to an end my employer was not in a position to renew it, so I was confused, should I break my visa rules and go underground doing odd jobs with no chance to come home and be with my family at a time when we needed each other due to the tragedy or do I go back home? With very little in my pocket but with ideas and a small network I booked my flight and came home. I vowed not to be employed again and start my thing and struggle with it. I'm not yet there but I have never ever doubted my decision I think it's the best I made. It feels good nowadays to get a job offer and show the employer a middle finger coz I got my thing going. Kids had to move from an expensive school to a cheaper private school but they handled it beautifully that I consider them my heroes.

with 500K you could buy a cheap car and with your mechanic skills
repair it then sell it for a profit. if you can sell a car after two months and make 60K that would be 30K a month and slowly build it as you look for other opportunities or build the business. Your skills in this area mean that you cannot be ripped and you can see potentials in an old car and therefore drive good bargains