A standard 1-2-3 would most likely fit both, yes, but I'd be really antsy about putting a 9 month old forward facing, even if only occasionally. Although it's legal it would be hugely risky for her if they had a crash. You could most likely put the 3yo in the harness still unless she is big for her age - do you know weight and/or height?
What about Joie Stages? It can be rear facing for the baby, it could be rear facing for the 3yo if you want or forward facing also works, and it's relatively inexpensive - often goes down to about £100. Once the 3yo reaches 18kg the harness just tucks away and it can be used as a booster seat although it isn't as tall as most boosters. But you can get a good high backed booster seat for very little money when you get to this point, or swap the whole thing for a 123 seat such as Britax Evolva.
I would caution be wary of the very cheap 123 seats which are on the market. Most of these are made by the same factory in France and they churn them out under all sorts of names, the most common being Nania and the own-brand makes (Cuggl, Halfords, Mothercare etc) but they are all the same model of seat and this model has been found to break apart in crashes/higher speed crash testing. Whenever there is a bad publicity story they just change the name of the seat and carry on selling it 
If you do get a 123 seat, stick to Britax Evolva - this can be bought for about £60-70.
You could also do a combo of two seats - for example Britax Evolva for 3yo, using harness for now and as a booster when she is bigger, and Joie Juva infant seat for the little one until outgrown (at which point it will be safer for them to forward face as they will be bigger). Total cost around £100.
I agree Diono Radian 5 would be suitable for both, but I'm not sure I'd suggest it as the best seat for grandparents as it is tricky to install and set up particularly if you intend to change it from forward facing to rear facing as it uses lower tethers in RF mode and top tether in FF mode.
If they have isofix, a spin seat might be a good idea. Joie 360 Spin is relatively inexpensive as isofix seats go (£200 at the moment, but you can often find it down to £160, especially if you look for offers) and has quite a tall shell so may fit the 3yo for another year or more, as long as she is under the weight limit. Or you could look at Cosatto All in All/All in All plus. The rotate one of those is a bit more expensive. There will be videos of these seats on youtube which demo how to put the straps away for use in booster mode, if you want to check how easy/difficult it is.
Which seats do you have at the moment? Sometimes it makes more sense to upgrade your own seat(s) and give the grandparents one of the ones you have.