I would try the qtl package. It is wonderful and has a lot really cool functionalities for genetic map construction. Here is a tutorial page on how to use it: https://rqtl.org/tutorials/.
I don't know what your population structure is, but Dr. Broman also came out with an updated version for simple mapping populations (not backcross). This one is called qtl2 and works essentially the same, but it can handle a lot more markers than the first version.