How would I feel if a parent suggested this to me?
I guess I would feel a little like I wasn't trusted. Also I would feel like this would be a difficult parent to deal with and would have to tell her that is not possible. Honestly after over 10 years in daycare, I have never heard such a proposition. I have had a couple want to come on the first day and spend like a half hour, but even then, I limit it to maybe 10 minutes because quite frankly a quick kiss and good-bye and leaving is the best.

It becomes harder for you hanging around, then your child will pick up on that, plus makes it harder for them because they need to experience you leaving and coming back everyday to 'get it.' If you're hanging out with your lg, she is not going to understand that you will still be leaving her but are staying with her for a short time.

Like the others have said, at 4 months I don't think it is separation anxiety, it is the new environment. You have to give it time and you have to let the provider deal with it. She needs to be able to take care of her and learn her cries and meet her needs so baby can trust her and the new environment. She may stop crying when you pick her up, because you are familiar and you are momma. Only 3 days at a new place is definitely not enough time.

I also wouldn't go for the suggestion of hanging out for 4 hours because that is almost half my day and would be too disruptive for our routine because of having a stranger here means the children will be disruptive.

If you have picked your provider and believe she has the qualifications to handle this, then you have to let her do it. You can't get into a pattern of rescuing baby (now or later) whenever she cries. Your little girl, as long as her needs are met, needs to be able to learn to accept the new provider and environment and if that takes a little crying until she does, then it's ok. She's not hurt and it's not going to cause damage to her, it's just new.

Give it some weeks and keep open communication with the provider. Leave something at the daycare that has your scent (usually a shirt) and try to keep her routine the same between both places and it will be ok.