Baby rental companies?
I always skipped the baby beds when we traveled. Okay, when we were in the car and we had tiny babies (pre-crawling). I always used the hotel's or asked relatives to borrow something. Same with the stroller. Someone always has one in their basement.
Take your own car seats. Do NOT check any as luggage. Use them on board. If the youngest is a lap baby, gate-check the car seat, do NOT check it at the counter. They get lost and broken that way. Also, never rent one from a car rental company. They're often dirty, old, broken and they may not even have one when you arrive (they're not obligated). Besides, maybe some other kid threw up or worse in it. Take your own car seats.
You might also do the "divide and conquer" method we often use. My husband drives and I fly in later, with the kids. One time we met en route because the final destination was too expensive to fly into (and had an awkward connection). Then you have your car and gear. My husband can make much better timing alone, especially when ours' were little like yours'.