mandy it takes roughly 1.5 hours in the car, if it leave at 7:30 I get into my workplace for 9am, depending on traffic (however I always leave later on a Friday, as it is much quicker on that day - about an hour).
Tram is quicker - if I get on the 8.10 tram I get to manchester for 9am. 50 mins.
Tram home I found much worse for some reason and tends to take me an hour. I wouldn't exaggerate - this is how long it has taken me from Alty to manchester.
OP would need to be in accommodation before she could register her DC because of the requirements of Trafford council. As the deadline is tonight, her DC would more than likely be on a waiting list due to the high subscription to most schools in the area.
However I have known several children get into our local school having been on the waiting list - lots of moves with parents in year R and year 1.
You would get a school place but it wouldn't necessarily be the closest school or your main choice.
Hale, Altrincham, timperley and Sale are lovely but not the only places OP should be told about.