How old are the girls?

1. How long have you known this man?  
2. What makes him the man of your dreams?
3. How old are his girls?

4. How old is your daughter?

5. Do his daughters treat your daughter well?

6. Most importantly, are you comfortable that your daughter is having a hard time? What have you done to help her acclimate to her new life? 

It sounds like you may possibly be rushing things. If so, have you asked yourself why this may be?

1. How long have you known this man?  
2. What makes him the man of your dreams?
3. How old are his girls?
4. How old is your daughter?
5. Do his daughters treat your daughter well?
6. Most importantly, are you comfortable that your daughter is having a hard time? What have you done to help her acclimate to her new life? 
It sounds like you may possibly be rushing things. If so, have you asked yourself why this may be?

7. How long were you in this relationship before you moved in together?
8. Are his daughters with you part-time or full-time?
9. Is bio-mom (BM) in the picture, and how is that relationship?

Welcome. Lots of knowledge and experience here. You came to the right place :) 
 

If he is the man of your dreams he'll help you and your daughter work through this and be happy to take his time. One last resort (but not necessarily a bad) option might be to live separately again until all the kids are out of your homes. 

Red flags are flapping in gale force winds and alarm bells are screaming based on your very brief introductory post.

Man of your dreams.   Why exactly? What makes him so dreamy?

Your DD is not happy with the situation. Why exactly? Is it that she is illbehaved and wants mommy all to herself?  Is it that his DDs are the Harpy squad and won't tolerate your DD and you in their lives with daddy?

If you wan't viable input, we need much more information than "Man of my dreams."  "My daughter is upset." and "How soon is too soon to marry."

WIth the situation you and he both have, as far as dragging failed family baggage into a new relationship, you may find that never is too soon.  

If you and he are both all in on the relationship and will put it above all else including his daughters and yours, and you can both immediately set and enforce standards of behavior and standards of performance with all 4 girls, you might have a chance.  Maybe.

Remember, you both have failed relationships in your pasts. That makes the odds of a successful second or greater marriage far less than 50%.  

Enjoy, but we wary, and do not let the tingle of new love blind you to reality and the challenging journey you are considering with Mr. Wonderful.

Good luck.