If you can't reach a suitable compromise (one that works for both of you and the family I'd be tempted to (partially) dismantle the road bike the day\night before your holiday and hide some of the parts. Make a note of where they are so none get lost and post the list to him so he can't get hold of it before going away and spend all night putting it together again. You can even arrange for some parts to go to a friend or family members house so he can't just look for them at home and put it together before leaving.
I can understand he wants to take advantage of Austria for his bike riding, but at the detriment of his families holiday, really? Stick up for you and your family, nobody else will. If he really wants to road bike while away he might have to hire one.
Is it too late to return the bike rack to the shop? If so consider putting it on eBay and, before you go away, plan other things you can do on holiday together so you're not wasting precious holiday time looking for what's in the area when you're already there; this can include a couple of days of bike riding using hired bikes, both mountain and road.
If the 'hobby' bike riding gets a bit much in everyday life and DH can't see it, try making rough notes of how long he spends out of the house for it and rough notes of how long he spends with the children, you, working, sleeping, etc. and show him how they compare. If there is a large percentage of his 'free' time spent on his hobby compared with being with you and his children and how much hobby time you get, then he probably needs to re-evaluate how much time he devotes to it.
I will get off my soap box now, I have a husband who can get lost in his own things\thoughts, but often when I point out to him how much time he is spending on them and how little time he spends with his 4 children\me\other things he likes he realises and adjusts. Time is precious and children grow so fast you can miss out on a lot while doing other things, DH prefers to see the boys growing and achieving things while he can, most hobbies etc. can be more part-time now and more full-on when children are older or you are retired.
Your DH enjoying a family holiday bike riding on his own will probably spoil a family holiday for everyone else, not my idea of a family holiday, something needs to be sorted out. I hope you can come to a suitable compromise about the holiday and you can all enjoy it.