I’d go with the Seattle UW (or the WI one- know about both of those). Excellent for CS and a great place to be. Different cultures on the east and west coasts so that is a real consideration. Campus culture counts a lot- life is so much more than one’s major. btw- quarter/semester credit comparisons.
Getting a job in Seattle does not need going to school there. Son from that other UW is now in Seattle- had honors math major (included some grad level classes) then added CS major to it. But- his UW is in the top tiers for CS as well. Son told his aunt he would choose UW (Madison) over Stanford- became a moot point.
Your D needs to decide which campus culture suits her most. She should not worry about a large sized campus. She also should be able to take her writing courses at either place. Not sure how those schools do it but UW-Madison only has comprehensive majors, no minors. Not a big deal as minors just mean fewer courses, ie less depth.
There is no rule that one can’t take more courses than required in one’s major that I ever heard of. Your D needs to look at required and available courses- with semester equivalents for a quarter system. She may find cross listed math courses in the mix. I’m sure that as a public flagship UW (WA) will allow for just as much of a liberal arts education- it just has a lot more to choose from.