How do I/should I convince my advisor to let me transfer with her blessings?
Keep the trust of every party involved. Don't lie! Don't disappoint them. Assume all of them are normal and honest and adult persons.

Ask, if you have a written offer, permission to forward it. Then do it. That might trigger direct interaction between past and future advisors.

Your actual (and soon past) advisor will understand that it is not his/her interest to keep you against your will.

Your relation with your past advisor is not a slave -> master one. Both of you are adults.

From the point of view of your past advisor, you are quitting (or giving up your PhD). That happens many times.

Of course, do respect the usual prior notice.

You want to be respected, and you should respect all others

BTW, notice that if you get (it is hard) some research funding, you can chose its topic. But that observation is even more relevant for your postdoc than for your PhD.

PS. The trivial point is that nobody is working well under constraint. You need passion to work on any PhD