I have recently become the holder of a blue badge and it very clearly states that I can park on single or double yellow lines for up to three hours unless it causes an obstruction.
Ummmm, your Mum , or you on her behalf, should apply for a 'Blue badge' so you can use it when she is in the car. Then you can park on double yellow lines without a problem.
ummmm, if your Nan is in receipt of attendance allowance or disability benefit she can get a blue badge with no problem whatsoever, so that when you take her out you can use disabled parking bays etc (as well as park on yellow lines!)
I don't know what she's in receipt of. She's 83 with dementia living in a care home. The blue badge would have came in handy when grandad lived at home because it's all permit parking or 1 hour parking. He's in a home as well now where parking isn't a problem so I only park on double yellows now when I drop her off, which only takes a few minutes.
I find a space as close as poss when I pick her up because it can take quite a while to get her ready. I go through the photos before I take her so she knows where we're going and what relations she's going to see. It stops her getting confused.
You should remember when parking on double or single yellow lines that the exemption only applies to locations where there are no associated yellow 'blips' or kerb markings which prohibit loading/unloading AND (the tricky part...) where no obstruction is caused.
The obstruction bit is tricky because it is undefined; what you might consider to be OK may be considered an horrendous obstruction to a traffic warden or cop. Also you never know what is going to want to go past; cars might pass freely but a FB rescue ladder might not.
I would say that if an alternative is available then use it because I have known cars displaying blue badges to be lifted and taken away.
Using your hazard lights is a no no. You are admitting to any passing enforcement agent that you know you are causing a hazard. These lights should only be used in the event of breakdown or other emergency.