I remember being relieved and a little freaked out when my T first offered me twice weekly sessions. I was happy because I felt I needed them, but freaked out because I thought that might mean that I was more messed up than either of us had originally thought. I ended up taking him up on the offer and twice/week really helps me a lot.
There's no right or wrong answer, Franki. If you can afford it and think it would help, by all means take her up on it. If the cost will add stress to you, it might be counterproductive. But I really do think her motive for making the offer is out of genuine concern. And talking to her about your relationship would be a really good thing. It can be hard, but it's an important part of therapy.
Hang in there. It can be a difficult process.