Wrote a long reply last night but then because of the awful MN Local system, it disappeared into the ether (only managed to find this again via @weegiemum's tag which was sent to me in an email) because I posted via the app (I should have remembered: happened to me once before
).
The Scotsnet topic is better to post in because of the problems with the MN Local system (which is why there is tumbleweed blowing through MN Local
)
But anyway, rant over: back to your questions.
Even if you are in the part of Lochlea Road that is in the Hillpark catchment, to date Shawlands has always been able to accept all its placing requests.
If your dd is 11, I assume she is going in to S1 in August? Not sure if it is too late to put in a placing request (or to register, as you're moving). Ds was a placing request (he should have gone to Bellahouston) but as it was so long ago (he's in S6 now) I can't remember when I did it 
It might be worth ringing the school and/or the council to ask. The depute in charge of transition and the S1s, Cath Sinclair, is always very helpful. 
As Paris says, you are close to a big Morrisons, as well as a good Lidl and a new Aldi. Shawlands itself is full of good eateries and coffee shops (although Nithsdale Road is my "local" for coffee shops as I actually live in Pollokshields)
I used to live in Shawlands in Bellwood Street in a lovely tenement flat and was very happy there. Close to shops, public transport, parks, pubs, coffee shops, wine shops
. Only moved to where we are now because we wanted a larger place and a garden (actually spent two years looking on the north side to be closer to my parents and dh's golf club before finding where we are now on the first night of looking on the south side
).
Hope your move goes well, wherever you end up! 