Will flap reconstruction impair looks/function of donor sites?

You are correct. Previous abdominal surgery does not rule out a DIEP flap. Preoperative imaging such as a CTA or MRA can ensure the perforators and pedicle are intact and usable for your reconstruction. My preferred autologous option in thin women is an Extended DIEP flap following surgical delay of the flap. This does require an additional procedure, but allows a larger DIEP flap, which includes the "love handles", to be elevated based solely on the diep inferior epigastric perforators. The tissue used is similar to a SHAEP flap but does not require additional vessels (pedicles) to support the flaps. This decreases the complexity and time of the case. As far as other options, there are a few. PAP flaps from the thigh and LAP flaps from the back are the most common in my practice.

I would have to see and examine you in person.  You sound like you have limited options.  The tope three locations are lower abdominal tissue, inner thigh, and upper buttock in my practice.  Although you can do bilateral latissimus flap reconstruction and hide those scars in the bra strap line it sounds like your activity levels may make this less desirable.  Definitely a case where I would have to see and examine you to guide you the best.

There are multiple options for autologous reconstruction other than a DIEP.  The best option is to be examined in person to determine what you are a candidate for and to discuss the potential donor site morbidity and complications.