You need to get a lawyer to represent you. Your daughter needs a guardian ad liem, this a person who is not affiliated with you or her father but is there to represent the child's best interests, because that is what a good parenting plan is all about. Dad will have and should have equal custody of his daughter in a perfect world. You should want and require that of him, he should want and demand that. That being said, until a parenting plan is developed and agreed to by both parties and the court, you will probably have physical custody. That means you get to keep her at your house, but Dad would have liberal visitation rights and possible custody on weekends. If you want anything different, you will have to prove that Dad is an unfit parent for a variety of significant reasons. Not being the primary caregiver is not one of them, as he may have sufficient support at his home from his family or friends. Even at 2 yrs old, she is old enough for overnight stays with her father. You don't have to be present during his visitations, and he could demand that his time be his time. (No, you don't get to tag along or intrude on their time anymore than he gets to stay at your house 24x7). Paying for visitations? Does he live out of state or a great distance away? If you have physical custody where it's difficult for him to have her physically every other weekend or other week, then it would be arranged between the two of you as to how the financial aspects of the visit would be handled, this would be layed out in a parenting plan. He could pick her up and you would have to come get her. As she gets older, her wants and needs come into play. Holidays, birthdays, school vacations, all those things need to be worked out on a schedule in advance so there are no surprises on either side. You'll know what your obligations are. It's important for him to be able to call and talk with her when he doesn't have visitation that week. And that she can talk with her Dad anytime she wants. The same would be true when she's in his custody. Parent initiated phone calls should be with reason, once a week or so. You need to discuss how you'll discipline her, what are the ground rules for various activities and who will attend school conferences, who will get report cards, have access to her medical and other health related records, who pays for what basic school items, such as school pictures, field trips, sports fees, etc. You also need to decide how much child support is going to be paid on a monthly basis, who provides for the health insurance, who determines what doctors are seen as some insurance plans don't cover all the doctors in an area, who will be responsible for those higher co-pays.
A parenting plan is rather detailed, and it needs to be to avoid any future problems when cooler heads are not prevailing. Her Dad is her Dad, just like you are her Mom. She's not a toy or a pawn, she's not more your's than his. She belongs to both of you and you have to, you must share her. Her heart is big enough to love you both without limits or limiting how much she can love one over the other. It doesn't happen that way. You'll come to know this when you have a 2nd, 3rd or more children. With regards to all the safety nuances, small stuff with big consequences if an accident should happen, he gets it. Have the guardian ad liem make sure when she does a home visit (which will be required of you and him) that she reinerates these features of safe parenting. He hasn't had to worry about them in the past because you worried enough for the both of you.
Again, you need a lawyer. Your daughter needs a guardian ad liem. You will have a parenting plan as outlined and required by the state of Washington when there are children involved in a separation/divorce/request for child support. The parenting plan can be revisited as the child gets older. Any consequences to noncompliance with the parenting plan will have to be addressed by your lawyer, his lawyer and the courts. I hope for your daughter's sake, that you and her father can but your interests aside and focus on providing a healthy happy environment at both of your residences, amongst all your friends and families. First rule, never and I mean never talk bad about her father and/or his friends and family to your daughter. That is her Dad. You wouldn't want him to talk that way about you and yours. Mutual respect at all times. Remember you wouldn't have this gorgeous, delightful daughter if he weren't her father. And he must remember this as well with respect of you as her mother. I wish all 3 of you peace and and endless number of happy days!