3 year old with blood in stool

I am a mom of four and one of my youngest is having issues.  She is three years old and has never had a formed stool in her life.  They are very acidic and if I didn't change her diaper right away she would get burned by the acidity.  Well - she is potty trained now.  Now that she goes on the potty - every time I wipe her there is bright red blood on the toilet paper.  Her stool is not black - normal colored and I never noticed the blood when I changed her diapers - but I don't think I would have because her stool is always so soft that it would easily mix in when in the diaper.  EVERY BM she has had in the potty over the last four months has had red blood or red blood clots on it.

I took her to the doctor and they said, "She is constipated and her stool is hard - that is why she is bleeding.  It is ripping on the way out."  Now - I told them her stools are very soft and unformed - she doesn't have to work to go (her twins sister has the rock hard stool that takes 20 minutes for her to pass) - they still keep telling me that she is bleeding because the stools are so rock hard.

I did put her on soy milk for a week - the bleeding stopped and her stools firmed up.  She hates soy milk and is refusing to drink it now - so now she is back on the regular milk and the bleeding has started again.

I think it is a milk allergy - but I am not sure.  My oldest has Celiac disease and milk allergies.  I would like allergy testing - but the doctor keeps saying it is just constipation and won't send us to an allergist.  Would love some opinions.