I would suggest you try to find a Babysitter mare- an old , tolerant lady, who will look after the baby. If this is not possible then get another foal- an older weaned one would be OK so long as it is not too boisterous.
A goat will do nothing to teach your baby it is a horse!!
You are on the right road with a bowl or bucket- I dislike bottles and so have all the foals I know- buckets are so much easier, anyway, and they "wean" the foal off the contact part as you can, eventually, just leave the bucket and go.
You need to start adding grain to the foals feed pretty soon- when I am raising foals on the mare I offer a feed of their own form ten days on and measure what they eat for the first month.
You can start this by giving part of the ration in pellet form and part liquid- but you have to be sure the foal is taking enough to be growing OK and you must be confident in your own mind about all of this before trying it out- it is pretty much the same as any other foal, once you are over all the teething problems, EXCEPT you have no Mama and you need to make sure roughage (ie grain, short chop hay, grass etc) is added to the diet.
Is it possible to stall horses of either side of the baby??
I am so very, very sorry you lost this baby's mother. Whatever the circumstances, PLEASE remember that hindsight is alway 20/20 and foresight is always very poor- not one of us here or anywhere can say we have never made a mistake, and not one of us has not got a day or two or even ten we would not like to do over differently.
When you can, perhaps you could share your painful experience- it may help you and I am sure it will help us.
I promise we are NOT judgemental- as I said, we have all been there at one time or another.
We can support you, anyway, whatever happened.
Don't beat yourself up, what's done is done.
The best can make the stupidest mistakes.