I agree, do not initiate any Valentine’s Day gift. I would have a gift just in case she initates, I think you will feel better having the option of being able to reciprocate the gesture (that’s more for you than her). Just don’t read to much into it, gift or no gift, and keep those expectations to zero.
Do have a fun day with your children.
BTW, the doctor was right when he said you are great H.
Feelings are fleeting. Be better, not bitter. Love the person, forgive the sin.