I’ve made offers before where the seller wanted me to get pre-approval from their lender. Both times they were bank owned and in one case I was told I had to or they wouldn’t review (I truly don’t think they did as I didn’t receive a counter) and the other time the sellers agent was familiar with my mortgage broker so they didn’t require.
If you want the property bad enough and the price is right, then perhaps you play by the sellers rules. If your really worried about providing your info to a new mortgage broker then just ask your agent to try again with your Penfed pre-approval, credit scores, and verification of funds.
As far as your agent relationship, just be honest with her and remind her that she needs to back off a little.
I agree with HLS about keeping that security deposit safe and not waiving loan contingency until funded.