Advice needed! Bonding & Litter Box issue

I have had my bun since the middle of June. She was about 11 weeks old. She would let us pick her up and snuggle on our chest, come up and let us pet her, us, ETC. Now she wants NOTHING to do with us except to give her food and water. She will jump on us or climb over us, but the minute we try to pet her she is fine. The only time petting can happen is when we give her pellets and she is happily eating those. She is not spayed yet, but will be. Is that her problem? Or does she really not like it's anymore? She gets time out of her cage(few hrs each day) but it has decreased a bit because the kids get upset that she wants nothing to do with them when she is out. I am at a loss. I don't want a bun that only likes us when food is around, I have cats for that! LOL. Seriously though, will spaying her really help that much?

Litter box stuff - When she is out of her cage, she had only ever peed twice. Both times were in a box that our cats were using to lay in. Pooping, that is different!!! We have hardwood floors and she WILL NOT poop on it, she makes sure it is on the rug in front of her cage or the large living room rug. I understand poops are going to happen, but we are talking the rug has no open area without stepping on poop. I want to let her out more, but I can't handle that much poop all over my house! We clean it up and 5 minutes later it looks like we never did. Is this normal? If not, how do i get her to go back to her litter box to poop? I am so frustrated and confused! I can't have her out as much as i want because of this. My one dog also keep trying to eat her poop. Like she walks behind her just waiting for the poop, lol. It is so gross and I do my best to not allow it. It would be so much easier if it didn't look like a buffet on my floor! Haha.

I am open to any advise! Thanks!

Behavior changes like that are perfectly normal when a rabbit turns hormonal. We hear this over and over again. The truth is that baby rabbits are almost always docile and compliant. But that behavior has little do with what bunny will be like as an adult (6-7 months of age).

Spaying will make a difference - ridding her of hormonal behavior and helping her be consistent with potty training. It is not unusual for a formerly potty trained rabbit to lose/forget that training when hormones kick in. Spayed rabbits train more easily and are more consistent.

Once spayed, the occasional stray poos are to be expected. Fortunately, rabbit poos are dry, odor free and easy enough to sweep up. OR, you could just let your dog do the clean up! (My dogs would do the same thing when the stray poos were around.)

If there is an abundance of the poos right now I'd expect that to be hormone related. Again, spaying should help. If she continues to do this after the surgery (after healing) then there is a possibility that she is feeling the need to mark territory - maybe because of the cats?? But let's not jump ahead yet. Perhaps the spaying will be the answer.