Please don't use Halfords/Smyths etc for fitting, they will advise on the most basic legal seats for your child, in which case you might as well allow the £10 booster.
Read facing is the safest way for your child to travel, if her centiles are under 50 and she isn't taller than average the Joie Tilt is good option, and quite often around £50-£80, however if your child is taller it won't last. It is a seat belted option, but not difficult to fit, and not any less safe than isofix (invented as a fool proof way of putting in a car seat).
Alternatively, the Joie stages is another good option, but again only goes up to 18kg.
Please do not alow them to use a booster, the fit will not be correct and submarining under the belt is a high risk, front facing is also not advised at 2, all you have to do is search for comparison videos to see why.
Can they not borrow your seat? I would be suggesting that as an option and being their only option, if you don't have a seat I would purchase the correct, most safest seat you can for your child and again tell them it is this or you don't take her.
My parents resisted on rear facing, they got told, they still don't 'believe' in it, however this is a hill I am willing to die on.
The PP who said it is unusual for a 2 year old to rear face......it isn't, it is 5x safer, just a shame people are in a rush to forward face, or as I see a lot have expensive cars, but the scraping by safe car seats.
The attitudes to car seat safety in this country is awful, fuelled by the delay in changing the laws and lack of promotion of safety.