....if you are sincere in this, you could approach the local churches of wherever you hope to stay.
i know this, because at one point i taught a group of about 50 children (for three hours a week), all part of a 'church' community. many used to come with their mothers and fathers as well, but the classes were aimed at the children. i'm not particularly religious, but was asked to do this. i didn't do it for free, the local 'padre' charged a monthly subscription fee, the equivalent of about rd$20 (today) - this was mostly used to buy books and materials and a few bob (to cover travel expenses mostly) for me.
they didn't give me room and board, i didn't need it - but depending how remote from the cities you go (i suppose), anything is possible.
one thing they did do for me (and for them) was arrange a meal at the end of the last class of the month. everyone brought a bowl of food or drink and we used to stuff ourselves. i had forgotten all about this until i read your post.
the churches would also be able direct you to the local orphanages.
i must admit to feeling a little uneasy about this....you have to admit your request is a little strange. i am not suggesting anything devious, but we do get a lot of 'rotten' (to put it mildly) people coming to the dom rep.
wouldn't it be a better idea to contact an official charity group in whatever country you are living in? i'm sure they would give you a much better idea on how to approach this.