I would like to take my mother on a two week vacation trip but I am not able too because my father is not able to travel? Any suggestions?

You can usually find options for short term respite care in an assisted living or nursing home, but it will be pricey.

The short answer is yes, there are. It's finding one and paying for it that's the tricky bit...

Try Googling "respite care in [name of your parents' location]" and seeing if any of the results look helpful.

Do you have a sibling that could stay with him?

I applaud your giving your mother some respite from her caregiving duties.