Six months from now your DD will be crawling/possibly walking, and real little wriggle-bum. How on earth can your FiL, overwaeight and a heavy drinker, even pretend that he could cope with a normal toddler, they wriggle, run or crawl away from fit healthy alert parents and put themselves at risk.
Your FiL sees your daughter 3-4 times a week? He shouldn't be complaining about babysitting and the like he should be on his knees thanking you for being able to see her so often. A very large proportion of grandparents, would consider such access heaven. For all sorts of reasons, distance, illness and, sadly, in some cases, estrangement many grandparents are lucky to see them once a month. My DGC live 200 miles away. We have a close relationship with parents and children and, even without COVID, we have only ever seen them every month to 6 weeks.