Suggestions for convenient and safe methods of transporting a few meals without a vehicle?
I think in general it is much safer to transport food cold (frozen, even) than hot. You can buy soft-sided insulated bags with straps - I see them in the grocery store - that should be ok for a trip of that length. I buy frozen food and then drive home for an hour with it, put it straight in the freezer, and would laugh at the thought of there being food-safety issues with that. So one approach is to make a lasagna, casserole, or the like in a disposable container, freeze it at home, take it to your relative's and put it in her freezer. Now she has a semi-quick (but at least easy) meal waiting for her.

(A side note from remembering my days with an infant: something that heats up FAST and can be eaten with one hand will be more useful than a serves-12-needs-a-fork-heats-for-an-hour option. In other words burritos (2 min in microwave, can eat while holding the baby) beat lasagna (60+ min in oven, you can forget and dry it out or burn it, then you need a plate and a knife and fork to eat it.) Samosas are good one-handers, too.)

If you want to take something that is ready-to-eat, you could use the same bag to keep hot food hot, but I would probably suggest heating it up again on arrival.