There are no 'secret rules'. University admission decisions have to be transparent, consistent, and fair.
If you are a mature applicant (ie. over 21) then each application is considered on its whole merits (ie. what have you done since leaving school that might make up for you having low GCSEs etc). However, what they wont do is offer you a place if there is not enough evidence that you have the appropriate skills in essential science or maths and therefore could not cope with the academic demands of the course, ie. that you cant work at the same level as someone with 6 A grade GCSEs and AAA at A level.
YOu will find that A levels are often difficult to study as a mature student now as most colleges will only run them for conventionally aged students and/or those doing retakes. This policy is usually related to college funding. Access to HE courses are usually easier to do, but you do need to make sure that the hard science content is enough, especially Chemistry. Check with a variety of Unis that the course you intend to do is appropriate in this regard before you start it. Remember you will need to achieve a very high number of Distinctions within the Access course to get the equivalent of AAA at A level, and you will probably need to get high grades in Maths and English if you dont already have this. No, you dont need to take A level Chemistry as well as Access (if its the 'right' Access course), and as a working single parent that's probably too much to aim for any way.
As you are probably aware, you also need substantial work-experience completed before you apply - at least 4 weeks clinical experience at a number of different practices and at least 4 weeks 'other animal' experience - farms, lambing, rescue centres, zoos, abattoirs, labs etc. This can also often be difficult for older applicants to rack up.