I presume that your partner is in the UK on a visitor visa and your son has Thai nationality. If you were to go back now with them (even if it was possible) you as a non-Thai national would need to pay for your own quarantine - at least £1000. Also you would need US$100,000 covid health insurance (presumably valid for a year). Such insurance would be very difficult to get. So your upper estimate of total cost of £5000 is almost certainly nearer the mark if perhaps a bit below the actual total cost. If you decide to split up and she goes with your son then you have no real idea when you will be together again. The penalties for visa overstay all not totally clear. If the overstay comes to light at the border upon exit then she could be banned from re-entering the UK for 1 year up to a maximum of 10 years. I agree with The Old Git that in your circumstances there would probably be no ban. There must be a lot of people who are in this situation through no fault of their own. Good luck.
I think a lot of people will be experiencing such difficulties. My advice would be to contact the Coronavirus Immigration Team (CIT). See website ;- https://www.gov.uk/guidance/coronavirus-covid-19-advice-for-uk-visa-applicants-and-temporary-uk-residents "If you intend to leave the UK but are not able to do so by 31 August 2020, you may request additional time to stay, also known as ‘exceptional indemnity’, by contacting the coronavirus immigration team (CIT). The indemnity does not grant you leave but will act as a short-term protection against any adverse action or consequences after your leave has expired. The Coronavirus Immigration Team will provide you with further advice on what you need to do to request an indemnity. This will include providing details of the reason why you are unable to leave the UK and supporting evidence, for example, a confirmed flight ticket with a date after 31 August or confirmation of a positive coronavirus test result."