S.T.
Seems that the grandfather (paternal I'm assuming) is very involved - does your daughter have a good relationship with him? If so, beg this man to intervene. Perhaps he can take her to see her dad? (can you afford to offer to split the cost with him?) If grandpa is willing to do this, before that visit you should allow your daughter to spend more extended time with grandpa - full days from morning to bedtime to get her used to being with him so the trip to see dad is OK. Also prepare her with photos, videos of her dad if you have any - maybe granpa does?
Realize that the possibility does exist that your ex may find that he really does love his daughter and this could be the beginning of a great relationship she can have with her dad. Many men don't feel a connection to babies / toddlers - but once their children become "people" and can communicate they feel very differently. If she looks a lot like her dad he may really warm up to her and her to him.
Is there no time that your ex will be back east to visit his father between now and next summer? If he will, get your daughter over there when he's in town. What about flying out for a long weekend to have your daughter meet him ahead of time? I agree that much of this may require you spending time and money on a situation that you shouldn't have to deal with - but wouldn't you do anything for your much loved and precious daughter? Of course, you would. Consider a flight for the two of you to the midwest inadvance of the summer 2 week trip to be an investment in your daughter.
If nothing else can work out then I would take a leave of absence from work and drive my child out there and stay in town if neccessary. Can it really be that you won't have ANY vacation by the Summer to do this? I'd go into debt - get my child a cell phone and be no more than 10-15 minutes away from her. This child has only been on the planet for 5 years and she's expected to go spend 2 weeks with a biologically connected stranger?
Finally - maybe you want to consider whether or not the child support is worth the aggravation? I do believe that children do better with an involved father who loves them - but if this isn't the situation here - then maybe you're best off doing without the child support.
But here's a thing to consider - my dad left our family when my brother was young - he didn't have much memory of him - but when my dad sent a package one year at Christmas with small present for each of us my little brother, who was about 6-7 at the time, said "wow he really does love us...." and he had just opened a .99 package of green army men. It could be that your daughter has quiet curiosity about her father - and it may help her feel more loved if she could connect with him.
Good Luck mama - I can't imagine having to be in your position and having to deal with this - my kids are 11 & 14 and so far I've never spent more than two night away from them... Pray about this and seek God's vision for your child and this situation.