Unpopular opinion but if you ask someone to babysit a 4 month old ( huge responsibility/not easy) , for free in your house, not their comfort zone and you don't get back until 3 in the morning, I think you should just say thank you and be grateful.

Unless you pay someone to stick to whatever routine you created in the 4 months your baby has been with you ( and that routine will most likely change 1000 times, because again it's a baby who most likely learned how to smile or hold her head up just weeks ago and things aren't set in stone ) you can't demand someone else to do it exactly your way. It's entitled. Be thankful people want to help out, It's not their job, it's yours and your husbands.

Also if you let your kid fall asleep in different circumstances, scenarios, such as noise, light. rooms, beds, songs etc, you will do yourself and your kid and everyone else a favor in the long run. Not just for babysitting but for your child to feel comfortable. Anyways, good luck.