2 yr. old constipated possible anal fissures

My two year old daughter has been constipated for about 3 weeks. Normally she has very soft stools and eats lots of vegetables and fruits. Lately she has been wanting more milk so I assume that lactose intolerance to be the cause. I am not giving her cow milk now, soy milk/nondairy.

I gave her half of a vegetable laxative and she has had 3 bm's. The first two were not very much, they were VERY hard and VERY DRY. The most recent was on Sunday, it was HUGE, very hard...the size of an adult's bm...it freaked me out, she couldn't even push it out--it got stuck and we had to have part of it dug out to make small enough to pass out the blockage. Once the big blockage was out then the rest came out, and then it was a little bit softer at the end of the bm. Her rectum is not prolapse, but is sore from it... I have been wiping with Witch Hazel pads to aid in healing and offer relief of any itching, then applying A&D ointment to it, also letting her sit in tub of warm water in evening.
Today is Tuesday and she is withholding again...sitting on feet, lying on tummy...afraid that it will hurt to go. And I am hoping that it won't become impacted again.

I have restricted her diet because of it...no meat, no dairy, no grains. She is eating all fruit, vegetables, some beans (not much), water, soy milk--at least until she is back to regular bm's.
I should also note that she had been given a couple pieces of chewing gum and swallowed them a few weeks ago...could that cause constipation?? Anyway she is not allowed candy or gum now.

She is fair, hazel eyes, thin-curly hair, sweaty head, turns red in face and sweaty when running around playing, very independant wanting to do things herself, is nearly potty-trained (which also adds to the problem, now she doesn't want to poo at all even in diaper though.)

Any tips for things to give to make sure stool is super soft for her tender bottom??
Anything I could give her daily for a week or two, to make sure that she starts going every day again?
Thanks,
Steph.