I have struggled with this kind of thing before. I found it helpful to ask my T before her trip why she was allowing me to contact her and what impact it had on her. I find that she is much less disturbed by my feelings than I am, so it's not distressing for her to read my emails, send me kind thoughts, and move on with her day.

My T has also told me that she goes on vacation to get a break from her daily routine and to relax and explore new places, but she doesn't need a break from me in particular. I tend to think that my very existence is a hassle and frustration to people, so that framing has been really helpful. She would much rather spend a minute or two reading my email (and usually replying) than for me to be upset and struggling for days in her absence.