I would recommend you search this forum.
2001 transmissions have a known problem with line pressure dropping, and require replacing the valve bodies and/or rebuilding.
The 2-3 shift is the most common sympton.
Unfortunately this is a grave problem, and not a simple fix.
I'm sorry I couldn't give you better news.
2013 XC70 T6, Premier Plus, BLIS Black/Black 7K miles, stock
2004 XC70 Premium, Convenience, Climate Blue/Tan 115K miles, 2007+ ABL lights, IPD sways F & R, TME exhaust, SS brake lines, R Brembo calipers & rotors, Akebono ceramic pads F & R (replaced PCV, power steering rack, struts and springs, end links, ball joints, A-arms, all fluids)