Let her go? No order yet

I have filed for divorce and we are early in the process, in fact my soon to be ex husband still hasn't seen his copies yet. He knows I filed and needs to pick up his copies from the post office.

We have a daughter who will be 2 on Friday. Her Dad will be here on Saturday for her b-day party and wants to take her for a month on Sunday.

Since we don't have an order I was told that there isn't much I can do. I can either refuse to let her go but he essentially could just take her.

My ex thinks that he will get her for a month every 2-3 months I have her. NO WAY will I agree to this. He is welcome to come and see her (we now live 7 hours from each other) but he has NEVER been attentive to her needs (part of why I decided to divorce him), cannot afford childcare or necessities our daughter needs (his mom will be paying for everything), he's on anti-depressants and while he's a good person, he's a horrible father, was a horrible husband and a lot of this comes from him being LAZY!

I know we will not agree on custody through a mediator and will have to go to court. I cannot afford a lawyer. I am willing to make compromises but he is not. I don't want my daughter to go but I also feel like this would be the only time for a very long time because (I have been told) no judge in their right mind would agree to 3 months with mom and 1 with Dad when a child is so young and a father is on medication, sees a psychiatrist, therapist, is not attentive to the child's needs and so on.

I am not trying to keep my ex from seeing our child but know how he is and how I used to BEG for him to feed or change her and he wouldn't or it would take 20 minutes of her sitting in a dirty diaper before he would change her.

I don't fear for her safety so much as just making sure she is bathed, clean, feed and etc.

I am to a point now and am getting so much pressure from family and friends where I am just going to let her go for the month because I know this would be the longest he gets her for a long time. Family and friends tell me NOT to let her go but then I feel like a judge would get upset thinking I was keeping her from him. My daughter is not a pawn, she is not going to be used to hurt anyone, I can't help that he was a sucky father and that I had to move away with family because he did not provide financially for us. He is WELCOME to come see her whenever he wants and I'm ok with him having her for a week at a time but I think a month is excessive.

Should I just let her go since I know this would be it?

He's delusional thinking a judge would ok for basically part time custody for him when he does work full time but has his mother paying his rent because he can't afford it let alone to afford a child, right?