For a 3yo, staying at home learning is the best! If your child is an extrovert who enjoys the company of other kids, perhaps daycare for a few hours daily for 3x a week will work for you? U can get some time-off yourself too. Another option is for u to homeschool her and give her some enrichment programs outside.
Montessori didn't work for my ds too. He was frustrated that he had to do the presentation from step 1 to step 20, and to repeat them till perfection. He wasn't interested in being with other kids too (although they were of mixed ages). Another reason was he prefers staying at home and do things that he likes .. read, play with lego, being with me etc. Even now at 8, if he has a choice, he would stay home!
Sorry not much help here. I hope u find something that suits u and your dd soon.
