They can if she falls within their managed move criteria, likely to be behaviour and absence
Not true. The Admissions Code specifically prohibits schools taking into account previous attendance, behaviour, attitude or achievement. The only exception is that a school can refuse to admit a child who has been permanently excluded twice in the previous 2 years.
The process for managed moves is a little different in that the parents don't usually formally apply to the receiving school for a place and therefore the school can refuse to admit for these reasons. However, once the parents apply for a place it is an in year application, not a managed move and the rules in the Admissions Code must be followed.
As she is not attending school and has not be taken off role she risks being a persistent absentee and then a school can refuse a place
No they cannot. The Admissions Code specifically prohibits schools taking previous attendance into account when deciding whether or not to admit a child.
They can if they are selective
Depends. If it has a formal pass mark for the admission exam and only admits pupil who achieve that score it can refuse to admit despite having places available. However, if it simply uses the admission exam to put pupils in priority order, admitting those with the highest score (a fairly common approach) it must admit anyone who applies if it has a place available.
asked them if they would provide transport for Dd to get to school and they said I will get fined for everyday that she is not in school
I am not clear which LA you were talking to at this point. If it is the LA for your daughter's current school they are partly correct. It is not their responsibility to provide transport. That is down to the LA where you are currently living. They must provide free transport for your daughter unless they are able to come up with a place for her nearer to your current home.
However, whichever LA this is, they are talking rubbish when they threaten you with fines. The legislation is clear that you cannot be fined if the school is not within walking distance of home (3 miles) and the LA has failed to provide transport or a place at a school nearer home. If they say this again refer them to section 444(4) of the Education Act 1996.
Do you think if I apply for the same school that turned us down through the LA I'll have a chance
If the school you want doesn't have a place available it won't make any difference. However, you need to check what the LA says about in-year admissions. Some tell you to apply direct to schools, some tell you to apply to the LA. If this LA wants you to apply through them you won't get a place anywhere until you do so.