nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpq9zsljfx8tjyzplququr9xmqctclx0qc2mw5xydzx0udqzrfade4qmtrtl5 (nprofile…rtl5)
Brouter can do that (on desktop and mobile) and is based on openstreetmap !
For instance: https://brouter.m11n.de/#map=11/45.5379/4.2345/CyclOSM&lonlats=4.244843,45.51433;4.292221,45.554234;4.309387,45.582818;4.254456,45.6267
Just drag the middle point and see the route change !
(Although you can't navigate with brouter directly, so that won't fit your needs entirely, but it goes to show it is possible !)
nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpq5lvqx4pfm4wgpnqd4leujrhey294ud8mlzhxq3lhtzyswcl28z5qnrmanz (nprofile…manz)