I'd be working out if the new tracker rate of circa 2% for the few years left on the tracker is worth staying with that bank.
If 150k of bank a is on 2% tracker for next 10 years and new part is on say 3.3%, would there be much overall difference if bank B gave you a 2.9% overall rate?
Then when current house sells, pay lump sum off bank b mortgage.
You may need to start on a variable rate with Bank b to pay lump sum off.
I reckon that if you do the calculations, there'll be little difference