I believe that you are misunderstanding some part of their offer to you.
You are saying that they are offering you a fixed 2nd at 4.50%? Fixed for how long ?
I could understand if it was a HELOC offer, but those are adjustable, not fixed. There are HELOC’s today that have adjusted to below 4%, but I don’t know of any new lenders offering them that low for new origination.
If it is true, take out the maximum amount that you can and pay down as much as possible on your 1st.