Just because she is asking for sole custody does not mean that the court will order it. It sounds like you have been an active father and involved in your children’s lives. Assuming no other facts, the court should order that your contact with your daughter continues on the same schedule you have been following.
For the court to order anything other than joint legal custody, your ex will essentially have to show that you have a poor track record of decision making for the children.
As to child support, you should argue that your ex is capable of working. It would be best to get the court to appoint a vocartional expert to evaluate her skills and to testify as to jobs that are available to her and what she can earn. However, this can get expensive. A cheaper alternative would be to show the court a series of recent job postings from the internet or newspaper for jobs she is capable of doing. If the court imputes and income to her, it will result in you paying less child support.
Please understand that this is advice based on very limited information on your case. I am also making a number of assumptions which could be wrong. The best thing you can do is to consult further with a family law specialist.
Kenneth T. Demmerle