Hi Helen Lancs
I do not know how the system here works for under pension age, but through experience, I can comment on health care for pensioners.
If mum is on any treatment, make sure she sees the doctor/specialist just before leaving the UK. She will be able to stock up on medication free of charge. Although normally you can only get 30 days subscription, if she speaks to her GP and smiles nicely she may be able to get 60 days to see her over. Also she (and you ) should ask for your medical records and contact the hospital for records of any current treatment being undertaken. You will need to take them to your local GP in Spain when you register.
About six weeks before you leave mum should send a letter to or preferably phone the Dept of Pensions overseas office and request an application form for an S1. This is a statement of her British pension and confirms she is entitled to NHS care. This is essential for her to get free healthcare in Spain. You will need to make a copy and translate the form. This may not apply all over Spain, but did for my region. Take both English and Translation with you when you apply in Spain.
When you arrive here you need to go to your local adjuntament (townhall) and get an apadronimiento (padron) for both of you. This is proof you are living in Spain whether you are a resident or not. (You must apply for residency after 6 months but that is another thing). You will need to take a rental contract, or proof of ownership of your house.
Open a bank account as soon as you can, and then you must take your passport, the padron and proof of your bank account to the police station to obtain an NIE. You will need your NIE to purchase certain items, and also for signing for recorded delivery etc at the postoffice.. Depending where you are living you may need to go to the regional town for this. Any local Brit will be able to tell you where you need to go. Ask your bank for a form showing proof. You also need a green card proving citizenship of the EU for your targeta (at least in Catalunia you do) which you can get at the same time as the NIE from the police station.
Go to your nearest social services office and they will give you the telephone number or web address to apply for an appointment. The one in my local town had the details up in the window, but it may pay to go in and also ask for the reference code for your area and the office reference code. If you have good Spanish you could phone them, or if like me you needed to translate very slowly, look online for the address you have been given, and then look for appointments. You will then receive an appointment to go to the local Social Services office to apply for the tarjeta sanitaria. After your appointment your mum will receive a paper document in the post showing she is able to get free treatment, which she can use straight away. Then she will receive a plastic card to use. ( I believe some areas only send the card but am not sure). She will have to pay for prescriptions but they are far cheaper than prescriptions in England. My average cost is a couple of euros each.
I hope this helps. It can be very convoluted applying through official channels in Spain, but you get there in the end.
Good luck with your move.