As the OP has probably figured out, liberty for plebes is a juggling act. To be clear, they're not in a monastery and definitely get time off. However, at the same time, they're in a military school that is very tough academically. This means WEs can be consumed not only by stuff they are required to do (duty, football games, varsity sports practice) but also things they know they need to do (studying being the primary one).
It's tough when parents have to come a long way and pay a lot of money to see their plebe. Puts a lot of pressure on them. They want to maximize time with you and feel an obligation to do so, yet have to balance what is happening on the Yard, in their company, in their classes, etc. Thus, it's really a matter of going with the flow, especially first semester. Things definitely get better/easier after first semester and especially after plebe year.
The other thing I'll add is that, much as you are sitting at home missing your plebe, in almost all cases, he/she isn't having quite the same thoughts. First, the plebe has (hopefully) seen family at PPW. After that, there is so much going on -- upperclass showing up, classes starting, parades, football games, and on and on that your plebe will be fully engaged. Yes, he/she misses you and home -- but it's more of a "I just need a break for a few days" mentality than "I really need to see my parents/go home" point of view. Always try to see it from your plebe's perspective -- does he/she want/need to see you or do you need to see him/her? Not always the same thing.
There will be Thanksgiving, which is always a welcome break. If there's not time for your plebe to come home that long WE, consider coming to the greater Annapolis/Baltimore/DC area (assuming you can financially afford to do so).