Hi and welcome to the forum.
Hopefully I can answer some of your questions.
First of all the residency part. You say she spends her time equally between both houses. Does she spend 4 nights at one and 3 at the other? Does this vary every week? Which parent gets child benefit? These might be things at decide.
It might be just worth ringing or emailing Wokingham, Bracknell and Reading admissions to see if they have a view on which one they see as her main residence. (I'm assuming you live in Reading and not WBC). Probably sooner rather than later if you don't know who will send the application pack, you might end up not getting one. It will probably be the LA that the primary school believe is her main residence.
As for questions about schools. Firstly if you live in catchment for ME you are also in catchment for Bulmershe, as its in part a shared catchment.
Currently Bulmershe is under subscribed and ME is over subscribed. You are not likely to get a place at ME unless you live within a mile of ME, despite the catchment being much bigger.
However Bulmershe is rapidly improving, has had a new head and £6million invested. Latest OFSTEDs for both were GOOD, with Bulmershe having some areas of outstanding.
So in short both are good schools. My DD has a friend from primary school at both, and both families are happy.
There's also the new ME (in Reading) which will open this Sept near Alfred Sutton primary school. The head of ME (in Wokingham) will be running it. They have a system of feeder schools in their admissions rather than catchment and were oversubscribed too, so,it depends on where your DD goes to primary school. (Feeder schools include, Alfred Sutton, Redlands, Newtown, St Johns, Early St Peter's etc), though there's a few places for those who don't attend.
You'd need to look at both to see which one you like. I thought ME was too big, but Bulmershe don't do German which was very important to us. (My DD is at Kendrick)
The Holt is oversubscribed and you definitely won't get a place from outside of catchment. Holt has a big shared catchment with Forest, Emmbrook and St Crispins. However you won't get into Holt unless you live quite close, (unlike ME, I don't know what the cutoff distance is off the top of my head).
Don't know much about Bracknell schools, except a colleague of mine has refused point blank to send his son to a Bracknell secondary school, claiming none of them are very good. They had been intending to send him to St crispins in Wokingham (just over the border), but that school has been over subscribed too for a couple of years and they had to rethink. They did put down St Crispins on the CAF but didn't get it. The DS will start a private school in sept.