Aww bless you I'm pleased my advice was of help to you. Bardsey is a fantastic school since the new head came in a couple of years ago. Before that there was a bad period and not great OFSTED reports as they had a few temporary heads that weren't in situ enough to make a difference. So if I didn't know the area and purely based on OFSTED I'd never have sent DS there! However, as I know the area and a lot of children from the school I knew the 'real school'.
I don't personally know of the two schools but all I can say is that I've heard some shocking things about St James' Primary, Wetherby from friends whose children went there. Apparently there was plenty of unresolved bullying and even though they help children with educational needs, they tend to ignore the bright children. My problem is that my DS is pretty clever and when not stimulated he plays up so St James' wasn't an option. Deighton Gates is pretty much an 'average' school from what I've heard. Neither good nor bad. Your children will do 'OK' there but don't expect then to reach their personal bests. I've always had an issue with Deighton Gates though after having to help a friend through high school as she didn't know how to punctuate and even spelt things like 'before' as 'befour'! She couldn't help it as she'd never been corrected but I had to do my work quickly so I could check hers before it was handed in! :D Of course, that was many a moon ago (more than I'd wish to remember!) and I'm sure they've changed now but I still worry....
I will ask around some friends about those two schools and see if I get any different answers and if so I'll update this for you.
Sadly, the schools I mentioned tend to be very over subscribed and places were awarded in January so that'll make it harder. However, try contacting Leeds City Council and explain that you want both children in the same school and with having the 9 year old you may get them both in after all. The trouble is that it usually only happens once your eldest is in situ. The only other alternative is to start your 4 year old at a different school then transfer as soon as there's space (usually within a year). I know it's not ideal but the nursery at St James' is actually ok it's when they get further up that it's a problem.
You should definitely get in at Bardsey though with it being a small village school. Also, the poor OFSTED report from a couple of years ago will help as it puts most people off that don't actually know the school! :D If you wanted Bardsey then you could move to Bardsey, Scarcroft, Thorner, Collingham, Wike, Shadwell areas as they all feed into the school (Bardsey, Scacroft and Wike get priority though as the other areas have schools but these 3 are purely covered by Bardsey Primary). Also in Bardsey there's the Bingley Arms Pub which is the oldest pub in England dating from 953AD.
If you want to check out individual streets please let me know and I'll tell you what they're like and what's nearby etc. The only place to avoid in the above villages is the Darkwood estate in Shadwell (Darkwood Way and Darkwood ?Avenue/Road/Place? Anyway it's the Darkwoods - that's a bad area I believe!). If you like walking there's even a nature reserve in Bardsey and plenty of fields/countryside yet it's an easy commute to Leeds/York/Harrogate :)