Hi josben...
I will try to be some help, hopefully what i say will make a little bit of sense. I just don't want your concern to go unanswered.
I am a Nursery Nurse and deal with this concern on a regular basis. Young children find it very difficult to share and turn take. Their Emotional, Personal and Social skills are very much still developing, therefore they still dont understand the need to develop positive, caring relationshipss towards other children. Your daughter is still only 3 years of age, she is still very young. I see you have mentioned speech and language concerns - this will have a huge impact on your daughters ability to communicate with other children, is will also lead to her frustration to share and turn take.
When speaking to parents regarding promoting positive behaviour in young children i tend to focus on giving the children small targets for example, use a sand timer and play a game which needs 1 other child - have each child taking turns (sand timer will help your child cope better with 'waiting' as it is a visual clue - she can see the sand falling, which tells her its almost her time). During simple things like this you reward her with praise, encouragement, facial expressions, sticker chart, small sweet, small toy - whatever suits her best. This will allow her to gratually understand that waiting and sharing brings good things in turn.
Young children at her level may prefer to play on a solitary basis (on her own), this is a very appropriate stage that many children go through. Play group and Nursery will build on her social skills through play and 1:1 activities. They will also have initiatives that promote positive behaviou in young children. You should ask them what strategies they use!
Once your wee once gets support for her speech and her ability to communicate effectively i am sure you will notice big changes in her.
I can say she will not be a problem child - she is a child who is still very young and has lots and lots to learn. Through time she will and you will feel better!
I hope thats helps a little.