Whatever changes you make, you can make them gradually you have two months. Start with timing how long your baby is awake before she needs another nap. My guess is at that age, 1.5 hours. Try to make that two hours of wake up time by the time she is 6 months old. Make note of what time she woke up, and it will give a good indication as to when the childminder has to put her down for the first nap. We all have our methods, but I tend to put the baby down and hush, and put gentle pressure on the stomach and or stroke the head gently. It would be difficult for a childminder I think to go out in car / buggy every time your DD needs a nap - so it would be much better to try to get her to fall asleep without the motion. Personally, I do carry babies in slings if needed but looking after babies and toddlers is very hard on your back so I try to do it for short periods at a time.
You could try to see if she would be happy in a little bouncer chair for 5 minutes at a time, and increase to ten minutes after a few days.
I also find that it is helpful if a baby has a reassuring teddy/blanket from home that they sleep with all the time, it does provide them with a bit of reassurance.
As for bottles, it is very difficult as many babies will have the same reaction as your DD. Would you like her to move on to formula when she starts or will it be expressed BM? If I was you I would try one type of bottle and offer it at the same time every day, and ask your partner/friend to give her the bottle. Not you, as she will be expecting to be BF. Warm the teat by spashing a little bit of boiled water on it, it might help. Stick with it. But most childminders will find a way to make sure that a baby gets the milk, even if it means spoon feeding or from a beaker. For me what worked with one little boy was to hold him very close to me with a blanket over his head, it is strange, but it did help him feel more secure I think.
I know that I have managed to 'train' babies to fall asleep in a cot at my house, but the parents couldn't do it at home... We all have our different methods, and hopefully your childminder will have a lot of experience with babies. Good luck!