Yesil Dalyan, United Blue and many other companies are
transfer companies in the market with a driver and a bus to serve you the best they can. Just because there are few bad reports does not mean any of these companies are managed badly because every company in this market serves to thousands in a single season and only those that have made some mistakes get mentioned or slated.
On the other hand, a good service, when recommended is considered an advert..
If you are not happy with the company your agent booked you with, please take it up with them so to change your transfer service provider, if this is not possible, either take the chances and try the mentioned company yourself or pay a little extra and use the company you feel comfortable with.
The majority of complaints in transfer services are about waiting in these shuttle busses for 2-3 hours to fill up before leaving the airport. These shuttles are the cheapest option to get to the resort so at the end of the day, we all get what we pay for.
As a result, my recommendation to you would be to hire a transfer service from one of the reputable companies to minimize the stress on your wife thus on your baby.
Wish you a great holiday.