Are you still in the same city as your T for the internship? It sounds like the only issue is that you can't get time away from the internship to see T during the day, is that right?
Two things...
1. You should talk to your T about it, if you haven't already. She might have some limited evening hours. Even if it was every other week, it might be enough to hold you over for the summer.
2. You should also talk to your T about how to approach your manager at the internship. This is a medical appointment, and my experience is, employers tend to be a little more lenient if you're taking off in the middle of the day for medical reasons. It might be possible for you to arrange something with your work, including that long lunch break, if it's just once a week for a "medical appointment".
I say talk to your T because he/she should be able to help coach you on how to approach your manager about this.
It was something I struggled with too, when I first started therapy and was new to the work-world. I had a good friend point out that it was OK to leave for medical appointments (since most Ts work normal business hours, it's not like it's an option to do it outside of those hours). He also pointed out that it would be a similar situation if I had been injured, and needed physical therapy once a week. Medical stuff is usually considered pretty personal, and it's nobody's business where you're going.
Oh... and depending on where you're working, long lunches really might not be a big deal at all too

Just a heads up!
Good luck, and congrats on your internship!