Therapy and friends....

Faith's physical therapist is wonderful. She loves Faith so much and has bent over backwards to keep seeing her over the last year. In the fall she moved over to the main hospital to work fewer hours and she quit working at our therapy center. But she offered to continue to see Faith during her lunch hour on Wednesdays. So NICE! After Faith was out during her surgery, she came back to pool therapy, just doing Mondays to help out the center. So we had her two days instead of one! Then a few weeks ago she called me one night and tells me she is leaving all together. No more pool therapy, she was cutting back her hours to just work three days a week. I should mention that her oldest son was dxed on the autism spectrum this winter, at ten. So I know she has been under a lot of extra work, stress and changes. But again she offered to continue to see Faith on Wednesdays. I certainly did not want to lose her but I didn't want her to say she would just so that I wouldn't be upset. We talked for a long time and she said that she didn't realize how much she meant to our family. She said that she loved Faith so much and wanted to be part of her life. She also said that she often thinks of us on the weekends and wonders what we are doing and mentioned that she would like to spend some time with us outside therapy.
She is so sweet and I like her as a person too, not just a therapist. She is very down to Earth and tenderhearted and I really look foward to seeing her each week. We talk about our kids and she confides in me about all the stuff with her son. I have often thought that I would like to ask her to come have dinner with us one weekend but have never gotten up the courage to do it. I worry that it might cross some professional line for her and be weird or awkward if I asked. She did mention how she would like to come visit us in the country. So I have been re-thinking asking her and her family to come over. Today, I got a text message from her checking on me (she didn't know about our crazy trip in NC, yet) to see if I was hanging in with my mother. I thought that was so sweet and I feel like she is reaching out to us.I know that friendships can cloud professional relationships and I am understanding of those issues. So my question to all of you is...Is that crossing some line? Or should I should ask her?
I certainly don't want to make things weird for her or us but I feel like she is making an overture. Carl says we should invite their whole family one Saturday night for dinner and a movie or some board games.
( I know we are dorks, right?)